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</style></head><body><div class = "content"><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">2.1) </span></h1><div class = "S3"><span class = "S2">Determine the coefficients </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">a</span><span class = "S2"> to </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">d</span><span class = "S2"> of the central difference scheme:</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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" width="258" height="43" /></span><span class = "S2">             </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="18" /></span></div><div class = "S3"><span class = "S2">where </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">&#949;</span><span class = "S2"> is the discretization error. What is the order of accuracy of the scheme? Is the scheme diffusive or dispersive? Assume a uniformly spaced grid ( </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="18.5" height="18" /></span><span class = "S2"> is constant).</span></div><h2 class = "S5"><span class = "S2">Solution</span></h2><div class = "S3"><span class = "S2">Expand </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="116.5" height="20" /></span><span class = "S2"> with Taylor series from the point </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="12.5" height="20" /></span></div><div class = "S4"><span style="vertical-align:-22px"><img src="data:image/png;base64,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" 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" 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" 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" width="682" height="54" /></span></div><div class = "S3"><span class = "S2">and substitute into (1)</span></div><div class = "S4"><span style="vertical-align:-151px"><img src="data:image/png;base64,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" width="324.5" height="312" /></span></div><div class = "S3"><span class = "S2">Next we match the coefficients in front of the derivatives </span><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="117.5" height="40" /></span><span class = "S2"> on the left and right hand side of equation (3) to obtain an algebraic system for the constants </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="53.5" height="18" /></span><span class = "S2">. We can write it in matrix-vector form as</span></div><div class = "S4"><span style="vertical-align:-36px"><img src="data:image/png;base64,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" width="226.5" height="82" /></span><span class = "S2">            </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="18" /></span></div><div class = "S3"><span class = "S2">Solving the system in MatLab we obtain</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">dx</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = [ 1  1    1  1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">     -2 -1    1  2</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      4  1    1  4</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">     -8 -1    1  8 ] ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">f = [ 0  1/dx 0  0 ]';</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">abcd = A\f</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="97ED20C0" data-testid="output_0" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">abcd =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img 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" width="75.5" height="166" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S12"><span class = "S2">Substituting </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="53.5" height="18" /></span><span class = "S2"> into (1) we obtain the finite-difference approximation</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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" width="218" height="43" /></span><span class = "S2">             </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="18" /></span></div><div class = "S3"><span class = "S2">In order to express the leading term of the approximation error, </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">&#949;</span><span class = "S2">, we also substitute </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="53.5" height="18" /></span><span class = "S2"> into (3) and obtain</span></div><div class = "S4"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="218.5" height="40" /></span><span class = "S2">            </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="18" /></span></div><div class = "S3"><span class = "S2">Thus the scheme is fourth-order accurate and the leading order dicretization error has a dispersive nature (scales with an odd derivative of the solution).</span></div><div class = "S3"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">2.2) </span></h1><div class = "S3"><span class = "S2">Determine the coefficients </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">a</span><span class = "S2"> and </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">b</span><span class = "S2"> of the following central finite difference scheme for a NON-UNIFORM grid (</span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="101" height="20" /></span><span class = "S2">const.):</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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" width="140" height="43" /></span></div><div class = "S3"><span class = "S2">What is the order of accuracy of this scheme? Would the order of accuracy change for a uniform spacing? Can you conclude any recommendations for designing a non-uniform finite-difference grids?</span></div><div class = "S3"><span class = "S13">Notation: </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="204" height="20" /></span></div><h2 class = "S5"><span class = "S2">Solution</span></h2><div class = "S4"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" 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" 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" width="232" height="212" /></span></div><div class = "S3"><span class = "S2">The linear system for </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">a</span><span class = "S2"> and </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">b</span><span class = "S2"> then reads </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">dx_im1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = [   1      1  </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">     -dx_im1  dx  ] ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">f = [   0      1  ]';</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">ab = A\f</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="71C916D8" data-testid="output_1" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">ab =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,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" width="104.5" height="82" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S12"><span class = "S2">Substituting these coefficients we obtain a centered finite-difference approximation for non-uniform grids</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQMAAABWCAYAAADL5fM7AAAUIElEQVR4Xu2dB9A8RRHFH0bMOSKKgrlA0VIRMSFGBAOKWcSAGXNCzIlgQBEDihkFsyCKYERQQAVFxYSlWCUGUEQRMVs//tPSLLPpbmdv77ueKgr4bndntmf2Tffrnu71FC0kEBIICUhaL6QQEggJhASQQIBBrIOQQEjgPAn0AYNHSPpQg9y2knTMguV6Y0kHS7pFzTheKulVCx5jdB8SmKQE+oLB3pI+KOmPmbf5pKSfLfgtrynpoZIuWRnHpSTtKOkjAQYLnqHofrIS6AsGz5P0EEk/mewb5Qd2FUkHJs0lNIMlm7wY7jgSCDAYR87RS0hg8hIIMJj8FMUAQwLjSCDAYBw5Ry8hgclLIMBg8lMUAwwJjCOBAINx5By9hAQmL4EAg8lPUQwwJDCOBAIMxpFz9BISmLwEAgwmP0UxwEISuIOkoyW9U9KzJP2tUD9L89gxwOBikm4naWdJ20i6Xgpa+qikfSWdPoK0IuhoBCEvWRcBBpUJKwkGPPuukl6e+nyTpG9Iurgkzjm8WNLJCSR+VHghBRg0C9jkc0932ZPSrunvvJqkDydQf2SK6iw8dcUePyQYEO7O+n6iG+3rJL1E0r/d3y4t6c2SHp9+e42k/xZ7w54PLgkGJqAzJb1W0l/c2NAWXpjOCRAe/IqK0Hq+RuvlAQatIhLzRbg5c8Fc3UPSsZXbNpP0cUmXlbSdpO+0P3ayVwwJBrwkaxqAfG96Y87IcGjOt2snAL2LpPtJOmRK0ikJBm3veWtJh0r6haSHSzq17YY5fg8w6CY8O5n61aS9nVa5bXtJn5FU93u3XqZx1dBgwFvZMzmw9yBJJ1Ve1db82TW/L1QyiwQDQ0kElNuFhhRMgEE3aUKkvVHS2yQ9R9K57jbWysvSP7nfu/UwnatKgIGB5WGSHiUJrdi3R0t6v6S63xcqnUWCgbdTS6tMaxkM2nI45BZYjkH39myOL7icpP3SIn92spEXunh7dI7t/soe13Np3/wcHixzfMFFk1n8oiQ7zOR/9BxT0cunAgalyagAgwsuoxwY4OWBHLx+DR9gv28p6c6Sjiq6Mod9+BhgcAVJ707qf25z87/vJOkDw77i/E8rDQY8/yaJPd1WErsYuRDel2xPGFgY7CrZUs2qVGejmtp1eNqxzqgRyVoGg/lXwbonoDZ/PpGCyL/KF2wh6QhJP03zdcpQHS/oOUObCaahoWHl+IJNJB0k6UYjmMUzibQkGJBt6BmSdpf0Y0moTrgWUTefkggqGGz+v6qSMS6Ya+wrUpjlbNQ+aleAQfvyML4AgK6qsMwHv78hZbp6asU7BCgzz7mPoL3n5itYI/dN7Dvr6Q/zPjDdPzQYGF+AtwXX4VmVcT5Q0idqyNc7SfpaAokjB3o/ewxeDjQ5xoSbvzYxUSkwYAAQUHskDYDF82v3kleSdICkB0j6TY1a6jmFnA3r1a7c716mAQbtH5z5yXOy3CCBAHEjuB75x/zjl0jzzI6XI81mXdsGArg7byPpC2kDmSIY8B0RN4ObPMcXXD4F2AGamBKA2jlOMAAt2hga8lAal4EA8kP7/l5blrJSYIB3AIQkVyK7xbcrK8Lv6mgLOdei2aib1qhVmB9EMW7UQe0KMGj+JL3/u8oHeGDnKaXJXvpAq+TjOk7SFyVBumGm8MFMEQw8uVrlA/jGHibpHUkLHoN8vYgkQJ0Qa76RHSTRb2PKwhJg4Hd9go1wR/2rshZtNwER69QqU53q+IK7Jxu2DkxCM+i+J3uPhDfZbCETTs7uhmpdwhRoGykEIH1PFQy8FlslwwFXNCYCuZ45gCmALNDU+pynQG6t+UtLgMHdJH0qzS5mwJcyM+2RtKp22uVNNizX2O85tavaZWgGzZ+bBwNsS0w4dhd2FCIN90l8ASDutbhd047D30tGJC4TGFhE7X8k4Xl5vqRXS3p6CuP2ckLL2jMR6101rqUCA1Q6NIKmKDXvpsoJwcd652zY9dPihIjcLdlpTcs9wKAZDLw2h2mHfckcEEkH97Nx0sJ+K2mX5FZksdNYnFvXRCy27fhdfy8BBl377nIdZs1ekgBHNIDvppv+mv4Gv4IngQA7eAGIRNOW2bXRnrtqXEsDBv4jbjoaaio+NiH2FCHJvrX5vPGFUwMB9RV+oo2BDTBoX9K3lESRGbQ55gX3L94c7E4O4GDzWjMANlDm79WIxfYeu18xdTDgTTZMxCofNW5Z5Ld/4s1svdsbe+8YmycmUFfydWnAwDP8ddWLurgEm3zemDaosgj6+6k4Cq7L0Ay6f1xDXWmnGD/XEJHYVomrleVO2sfQnMFQMpjnORb1iTZRF5FoLtCmftqiJRfCGXguoA4MbFe/rqT7Szo+85a2E+X4gJumk2FoBXXkY/WRoRnMs2Tr77WDN6i+JSMSl0EzmEXCpgGjRXeNSFwazcB7CXLEIFoBhAqcAgEsuI/+npGihY9WTY1rSHq9pBOSSvbWzJnx3KQEGMyyVNvvYceByB3SP57rda2CAbs+ZQnhzarHxeukvzRgwAtYpBUehce5k1uW7OQ9iWBh9/9dzRsbGOBjJlCDwCTqKBLQQfAJ5gg2bFefbYBB+4fd9woz964jqRqR2PdZbdevVTDgGwBIc+HfawIMLpOYVQgRMrlQ45DsRgQ84OskLoCPuKlIqwEKAjkxBZqgFRBOSfw82gGeBDQDtIs/B2fQ9j0N/rvxQwQB9fF59x0I64noyNsmsrl0Vqy+45v1etOib9YzfqKvZmCJhPheiIH4ct2AS8QZ0BeuFuLJnyyJuAPcVYAAdtFnOySfxCuBC4tFBg9BQg0WBIShj5ajL7LttKmpoRnMumTr7/MRoLDjALXPfzBvj6jOLGDsauIgaOb2PCZtNEP2N+94+97vU8jhGUO7quY/6PtMfz18DuY4/WyefjC3J+cTMNcv0F8pMJjnJUrcuwgwQLZMAizxvZK76e0pNh3/c7SQwKQkEGBQbjoIQ8VPz87mG5oR5pJ3h6LK2WEuCCUL6Ck3unhySKAigQCDMkvi6sn9efMUE4GdBucBV/LcdIyUEFUi0WjYcnhXAA/Ut5XP4V9mWuKpTRIIMCi3Pm4v6VrpnIYd97V4/70zGsPHUvx6nYel3EjjySEBSQEGi1kGN0zJQAj9JXQ1uITFzEP06iQQYLDcy2EyBTiWW4wrO3qyK1HD4bwWYFBuHSBbcjJwhh33agkNIMCg3PytwpOLgQEI85UFS5C0XBydrraxXYt4Bzh6jZ+XOAnfct4EEocQpEUchq88tWBxRverJIEhNYMAg/NXDhoB4dhEWZLUgrRvhFPnvAmQirgaOdNOdBkh174+3yqtx3jXBUpgSDBY4Gu0dr0IzYBzGYCAr0fY5E0gyrLpvEbrS8YFIYF5JBBgMI/0Zr/XexMIsSU3Awev+O9oIYGFSCDAYCFij05DAtOTQIDB9OYkRhQSWIgEAgwWIvboNCQwPQkEGExvTsYYUVOprzH6X+U+fCbqtkpgo8ppTDDg8M6OKSU0J/rwp3MunQM6HOQpeVJvbG/CqJPYszOShZAU5jHpvi7ZpXt2EZc3SMDqihB/8sERskR1nowxwODKKY02QTWU/P5QSmPGiT6yFLEYOfMPKFQrL3V+kZYLAwzOFxAZgz6dDlHx11xtwKHkHs+5oAR8fQV+IQ6la72E4rIcAwxI+rhfQkCyHfkQWjIdk+WFFFAPlvTDQm8cYLBOsFYglCxUpyZNranYTaHpWNnHWuWqkyWR7owK45MxFcYAg6aZ99mUuyY3nWUlBRiskxpHqgl5ZjEe0qEM3iyyXuZ7rMZDXZr/ed+NQDTKr1GijlR9BJlRbOVpkhae/WrRYIBwrUaCrzIzr9Cr9wcYrJMIxCGLj6PTFC/BZiUlm9UHXPUw6JJgYMThWenjp2YIJjMJXktqxZ2/pSmAgU1A14IonV/OXRhgIBlxSFZjdigyStt5CJ+SvipfK5SCVkHj/ARZrzH3WD88g3+sLTMHURIMjDiEuCW1HZwZCW0wla3YbW5tb58SAttvvsqzVWTifmszmx1TAgPqIQxZctsLNsBgXapxiEPSzJNpmo/ZV8y+d/Lu5BYk1a/ekop9HJ5OWJ6RLmTHgxOiZiY8xGPT6dVlPF5dCgyMOKQKmNUW9V6dprqkfKObppB17q9eS45NNLw7phqZAMMPZtkxxwIDXpzU13gUIBRplGpngVGEAzv2MFd80nMJXFutx2dpuhESrY2VXXUwoOCJVfr1KqlPO+93/NxaMjC5bDIzmD+aqb+3WnIg4F1KgYFpAWi/VBozc8xM5C71Ji02pGpWWLlCxj8zEHDzGGCAIECzzdK/SfpJnr8tkq1K/AEqaBXxyAkA0YJPHJ+sV48Y931SDQbeg7RhL2jIBbDqYGAf/Ukp4aqVtPNFcKs7fhUQfIVt4xiIDWGno2bCEySRLGOZWykw4KMHjKu1RfkmAAgOrvn1nZMh38m7JGE2mFnBN0L1azignRP/MLP8S4OBFUnFjUJBDOIMfHCRr5yE6lqtROv9slXW1e5tAwKEs+pgYLLaIdmrfsFYuXCCwJpMBe4xs4Jj2SxeVFO8QM+Q9M2ZV+H4N3pg69p7l9079yzTnPjNlxvk/32h4iZTwZ7L/RQjxixA5oDC1pJ2balQ1ukdS4IB2Xv2TbUS64qsemSscy2SKOQgSX9yrCtpxxHer9NO1+aWWWUwMNsUc8zqVvrFYZWAt6yQg3ULG7ljasCEb5KYcZ+zodPCW/BFY4KBASjVwQ7IvDd/f2PGFM6JaKMkd7QEqouxWVJvA65m7lYSDLyNg08VFbXaPFMNp4Dvu9o80QJTCgkGyMATkFasDQhWXTPIEYdexp6fqRbLzS0wm9evJ9OAUl1rpQ1tJuSIw6ZvIKe5+ev5XgEPNlfMC4Dg90MJvxQY+A+4KajCVFRQjnMLvsqQf0eAAtWIzEFkCyLX4l49io2sqmZgxCHqZNVe9fI19xXVrpuuI7R8jwQC7EaE0jIn1WYuL9u5hs7rCMeEyozHAjfnUG1oMDDi8MgKV+PHawVskSWEOkV0jNOpvhdaHJ6bbZPnB1Ptl5mXtzqO30raXqf4kVJggPqIas/O3+T3NBWpLcbAn/SCMEFofc4xrCoYGNMMA90U5WbX4bpCvuZ69Otsg/T3n0v6Z1pkdcFKZnqQ/JW4g6GagQDrBmAaOlJwSDCwXRxyFYLPvC9VWfjd/jjneqxeB7DAjx0qaeMUrFcXn2AaN3I6uKvwS4EB7sOj0yC2qvFfe/KkbgHyCMZIlByCYJHV8Q9N77yqYNBEHHp5eaI2B8y2I3HKFPuWmHrMtV81LN6ua7DrdTdIRBmcBWXgD5R0VPJIdX1G23VDgkETcVgdhz88ljOX+bjxqqEVQMKjvVGar4tZ1/bO//+9FBiY2tnEwBp5iN96u0riUBsgJgF8A7UHEAYeCYjJvuGbqwgGZqrh0bFAl6aFYR8CpoKfD9xeyP4UR9Z61Za5QVMbM8io1HwOCQZGHKIZ5DQtPxdXdaHhVa8aZfrYCDnQZyd7TfMizobYHZLpzt1KgYFxAXVg4FWjOjsJH+pOyX2CDxvCEJ4AN0qTJpETSqnFM/cEFHyA7TacSoTFbrMbN0zxAuzA5tkxIEA9r3I6ZuLB37Ag8eywG+6T1GIiSlFjicUfupWaz6HAwDQtNrLdJGFatTVkSPQmJ3uJr4GTMSA4Pf2Nf9M86UvAHun4CS9n7vie4BRyrvrGMZQCA7NZCFnNEYN2lPOKNSSUFSHhw/fBLKZxoK7WkScBBpIRh0QVztIwFfDUQBaSbwLOAXmf4B7m3cLsXOSmONPFdHAt/beB0CzjKwUGs4wld48/dzDLMzEV+PCRKyYZgMuZBswya7bh8v/Ino+f6t32bXEvJlXnVgoMPOFXdZfAFeyZFhfkIuqPVzF9NSLsU8I37XfvE98lBWB0UU/nWTwWvUd0nR9LZyEv4EJ733vO2DcaHQuJk6TWqlyC53y4xs6WMPeQx1Sa7kxe9RznPPPZs6uZLjcNY6abEzF6duJn7BnVnd6HknONBS0BHpgNAMqxfQZQCgwYA6nNCD3GD437h92F3QQbkwCX3VN4pfcKVMuSwUTzAebCZ1GjUEO7pEybZ/GYlgNw5eIg+sh7Fa61ILE6HqhLwE9bNN4887nW54DAMsKfzdTo/L4lwYBBEDGFqg+rza5+YlJ5YEV/kSGdPDFlL1FlV716xDVtMd1cE4un85KY+0K4BM6NsBjNxp37oZUHxHzmJWpcAlob4crn9BF8aTDoM5aS18biKSnd859tuz48ASTvuYW6jfnMC9a8Erhce8d3BBjUr1aYWdTVbSJpaOdP2uxYOINe5FXnHtZdGGCQF5iRuoQpE/XYq/UFA0ghwoJzNQHJ3oL7b5GNSse4c3Dt+MaOhVcDspKoua7N8iaQEAQXTrRmCRi/QlVpgoJKNUuke3yK1e9yPqXUWKb0XPO21QX6NY61LxhwUq2uzTSAgSVpbhUY1VzrG74KGUZILe61XszswO+1LI+DvII0htyFOyBCbqi2fnKhEd3K/BKOTIOgpj88H4ME3ww14JGf41PQIRM8Gr1Ok/YBg5HfbRLdwcqiaSDY0yYxohhESKCQBAIM6gXLTkT4Jwxtb2a20HzFY0MCxSQQYFAvWiPDjpiFmS02Y/HgkEAhCQQY1As2go0KLbp47DQlEGBQPy+QYURJTqYW3jSXUIxqrUggwCA/k5Y1ePNKjYC1Mu/xHiGBC0kgwCC/KCySi/MU1YzNsYxCAmtSAgEG+Wm1XACkCiOYKlpIYM1LIMDgwlNMrj8OUnVNw77mF0m84GpIIMDg/Hm2JK6kYSOj8/41YdersTLiLVdOAgEGKzfl8cIhgbwE/gd4tMqim5HA1wAAAABJRU5ErkJggg==" width="129.5" height="43" /></span></div><div class = "S3"><span class = "S2">Substituting the Taylor expansion of </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="27" height="20" /></span><span class = "S2"> and </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="27" height="20" /></span><span class = "S2"> we can express the discretization error</span></div><div class = "S4"><span style="vertical-align:-36px"><img src="data:image/png;base64,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" width="435.5" height="60" /></span></div><div class = "S3"><span class = "S2">One can see already that the leading term of the discretization error vanishes if </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="71" height="20" /></span><span class = "S2">. We would therefore conclude that the grid spacing should not increase nor decrease too rapidly in space, otherwise the discretization scheme becomes too diffusive (due to the even derivative in the leading order error term). To see the order of accuracy more clearly we define a growth factor </span><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="59" height="40" /></span><span class = "S2"> to obtain</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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" width="420" height="45" /></span></div><div class = "S3"><span class = "S2">The scheme is therefore first order accurate for non-uniform grids and second order accurate for uniform grids.</span></div><div class = "S3"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">2.3)</span></h1><div class = "S3"><span class = "S2">For the function </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAAAoCAYAAADtylhqAAAIbUlEQVR4Xu2cedC3UxnHP2+pxKRCDUajoihSNJMllEaWKUWlEKIYWghZQsleMZZWla1VNW1DZVIktDAY2kZNmBhjqQgtlqGaj67zOu/tPvd9P8/z2/44Z+aZeZ/nd+5zrvs633Nd3+t7zu9dRG3VA2P2wKIxj1+Hrx6ggqyCYOweqCAbu4vrBBVkFQNj90AF2dhdXCeoIKsYGLsHKsjG7uIFT7A8sB5wCfCfBY+2sAGWBjYDLgfuHzpUBdlQT02n3wuAfYHjgTunY8LjZl0H2BX4OHD3EJsqyLq99Hbgq8CvgbcBfxzi1BH1WRM4EDhyhgCWXu1FwO5DgVZBNpsgexbwCeDzwKUjAu2oh9kReD5wIvBw1+AVZN2ufyPwHuAe4DDgplGvVMt4T4wI9hTgY30LOAF7SlM8FTgF+BFwXgXZFFdiHlOvDXwKePeE0/M8TOUVkc73Am4vDVAj2XxcO75njGIfAZYCPgw8Mr6pRjLy04DPREo/q4JsJD4d+yCrAecCRwE/Gftso5lgb2Ar4F3A39uGbItk5tpTAR9O7aMtO2uZIKd7xmeW2f8djd1jGcV3XQvQ3s1De3Iiy3Crx19EtfRP4OXA1wArPNuFgJXmXfG7epFAkK+5m227xDOS9vfH72pcFwOnAZcN8M8bIv1Iqm/o8ILvsm7IG1sAgnNo+yWwM/DSBpdK9jtOvrZp3H2iEGnOsyHwDeDNwDVDQWY/w7WTnhMP+dLfbAywSjj11YAE+fyhbxn9XEDH9GWHNqutA+YiBMbAvo9OOgH4QSz6jcBy4fBDAZ2fA2nZ2GzyjSbIkr2vCYljZUAf3RLpQ6DaXhYgvDnGFsilZqo8FlAbcyPcW+iYv8ttwF9iHjfLnzLB9knhW4F+LfDXGO+3kZL/DbwE+AKwQQAo963A/QqwKXBl2PS7FptS9HVtvjwXkNn3lcDPw/C3AL9pDOBu/z6gQ9s+7wPOJEEmmf4W8LcA1a2ZcS7aByK65SCzS9LJSiBbITaa6cJK67nAwVGFGm2MmGdHpDE7fBB4qOCYxG+0sdTPMfcDXgW4MYx268c6WCyYcVJLiy+QtgSuKMz7JuA7wPXADsDvo9/zgK/HvwV9G8D8+OnAmYGTVh7ZRfwN3ZamPwyFt5lvdwO+1PF5H8gm+XkCy0UBsrSr+2yYC8j0k4txRzbok0OGMEKU/Ji6m2blY6ZVI1opKAhcgZBOAJKNzWxiGvtxpDD7GPXa2rOBMwDXW/sl8GnjbQ/sEQAs+SrRKyOxNMEIuUQrgcy/W+X408bHUmhXO+rboX0LOYnPXxsO/0ekWzdHp4AYRs0FZCXOIsCMcqVomN4/RfbTC9ynzU9pHV4PvBX4Q9ZJTv25iDKti5/1lbQbjUyP9hVsUgGjpim4q8lPTwZWb9CNxc+UQJZCoGmwjW/ln7+jlIsngZ6Bcxgl5AzuTNv3YnP8qgdscwFZTpxzs/rGaILspEjBQ17tmQEM+3qemLJNHkE9mjIQdDXTvMdnRjU5m0LwewG55JBmmpReNenGo8+WQJZ2lVVGG99aIyqKF/bk+yEGTqrPSnHQ/M5swquiorQYeLDFkD6A5JxsGiCzwvx2FDM5j1sxwLd1rE+fHCIOjLhGJMcTYBYUQ9u8QJb4mBO2VTqJLP4s0FvK911GTpL4JzueALw4jm3cPEl+MLLp5ObOnQbI5pIuk33NbJLAJz8acrBvkaCo+rqQctwwfx6IsMTJVi1w99ZIJqqPCPLZxscs+61kJP7m8b58X7J1GiDLbVF2UJ44KMD2ReB9wL+yTpME2RDin9ufUqJBoFk9Ciy1q1KQyMex8hbYKgXyKrlcKgCG4CyBzL6t8lJbukyltDm+uUPsv1MQSvsNyfdDDJ1WH99Hh6oVtV3nmSTIhkgYuZ+STinYFFdTFM6LtqMBf0oiuTLUpyOKWdluF3KGkb2o4DcWK1EGJZLWudpA1sUz1GcEn1Xa/gPz/bQAlOZNO03OdUgL91IwVSfynZqpZZIgSxlEcbpLjE3vlSrmZjbJi7I2ET09v1FEMLUwuZjVdq6tuc6dtytioMTPLViagn2R+OcgU68RnV773TgW6bjsOGPb0lHCtJGVzZ9AJgmWh13dsG0b4IKoOJu7N2mBJX0tpTiPdkpV9lw0OoHjYvXxKKs/73EpMRzeEGHz9dskOJZRUhE4FTcJYOqFRsGkG+ZVqeq9t3Lv61lLbfbuWy7kLvFIWyTLX8DdfV08IVfxpQy95ntDrTvFKDBEc5oW7vKzWFPiMeF47bHs9ubpMwIk+QXB/FjJayyS4Z82XiI/VlLQlJPknM65BYNcrzRGkye6uHKk73Y4LJ+3KTElWUMSL6f2nQWSPFvVPgHMiOn3Brzh6nFYM0L6u88of5Tu86foK5dr8tnFA5YkjOdEBHPnWzlKiuUtno+lMJ0G+WwcyzwwLRT1zKtg6Ybw6EcVXKKbDpTlEUYpVe68mnKh1NXcnan57kZ2D7ttam6mKs8GU3MsibOXG9vGcNN6sK4429aSlKB9bandZ/JNo6bVFGEdQ24lwBRK1b+MNClaJXE4zd8U0/Mzaft0nRdbPIkNMVBMrfU+2eztDIVRF9Yo0kzts2atUpaRtDOtVpDN2rL9XyC3gvdrcB8qiMSzYLWnA1amRsmu2yX1P1yZhdVqscGU6FfOvH4k/521lg7QpUif7LsnVyPZrC3fY/bI9bzO46F16ZrNNKwXM1bqnpwYydqO45awq4JsGss0fE6B5l03K83WW6fDhxpJT/FiAeX3LiX7vQBz1gqykfh+rIMoKVnFqehP+3q7tliY5Ddwe1++gqzXRbXDQj1QQbZQD9bnez1QQdbrotphoR6oIFuoB+vzvR6oIOt1Ue2wUA/8D8heFke5ZthaAAAAAElFTkSuQmCC" width="76.5" height="20" /></span><span class = "S2"> compute the first derivative </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="13.5" height="18" /></span><span class = "S2"> at </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAAAkCAYAAAB2UT9CAAAEPUlEQVRoQ+2ZaajOWRzHPzfKnvCGFDNlwhsKIcsL+4uxRINsZc2+l0iWIUuKsQ1N8caaIlsKEUK8YIqUkZGlsYU0Y3thm77d37/Offrf5z7/5T5/uufUrdvznHN+53y/5/f9LU8JfmSKQEmm1r1xPAEZPwJPgCcgYwQyNu89wBOQMQIZm/ce4AnIGIGMzVcVD9A9WwETgZ+BlsAd4ASwBXiQIg+1gHXADGApsDLf3lWBAN1xOPA7cApYCzw3IgSQxlTgJPA1BSIGAbuBep6AUjS7AnuBW+YBzwxkETPKwLoBjABuJyTgB2CP2dRWVd4D6gBbgbEG/s4cgJsAu4DeJhW/Ap9jklADWAV0AL4APTwB0BE4ArwFfgFu5oBbzYBfBJw3j3gSkwBJzybT/v7AZE8AzAU2mPZLbl6FgKvPJRtvgL7A1RgENDUp+9O8YE0SAtoDxwG5p8YS21QBSrq5zP6Cc8qY5sR13Rj3LWhJTWA9MA3YAcwG3oesVIy4ZJ+PtnhRkAGbVB2QdPUCxgD/AL8lIUD7NgM2A3IrZQfa+KUZbGAZhYLWQ2A8cC5CBiGyVkS5IdANuBxxjc6pbERp5x+UesOHkD3aAAeBnwqRjJD18hqtF9EK9iI+MQGyE+hnXWAwcNYhQMGsXQzwA48qBgGNDJB+FRCgmuAA0DYGAY3NuyRtM4H/ANUBqRDgbqRiQm6m6K6XvxyYBFyI+CqLOd0FNp8HxCVA0rPQsisF+Gt2udQI0H7StcPAdUD62B2YZ3p6pZhoxrBV2QT0tOC9zYq7T5VBgHRUr2eoGWthaZYI+dZHc2Af0KUSJCiQntoWHx87YIR5gHCUbCspKBPLCmlFDAEOARdNdtRD+R5GnBgwxcjKdz9Jz3x79eMsY3TnKwhLsvXdaktmJFETgJHAX+7kighoaIak98p4XK2LS0KxsiD1YtT/UQanLEWNuH9DDt0ZOG29G2V9xyq4mEtsFAzU7lBPqswDzkeAigtF83vAR8v1g2CcJOcvFgGFVrl9jIC75VTLUUDW3FSCsPRTr0d6pUpSKZpK+keWBd2PeqqM5gfy+RQYYMlE7lGCajmfl0Q5fmICVJCogfU3sAB4B9S3fFcSNMd0LY3WbZSLxZn7I7Af6GS6LY92z+3KlCQqt1kXx2YiAgLw1YYYlhMwgpeiqle66kb+OActxhpJ7Cxgo3mzUmn3x5egij1jrYMXOYcK+kT6uNBq3K3AI7WjA/B1KPXFdVg1l4LhluzbgcXA62KgmNCGWtJqE6sXpGCr/3U/1TTKUtRiUYYSlt3FIaC1eZ1kW943PR9ObhAeCBx1Lpuria67app+XSqvw5gQs9SXq1ev/rz6Viould2pilcLQr8HSGbDRlQCJM9KMrR/MESs9gmtnSpKQ1NHwm9YFgFPQMYvwhPgCcgYgYzNew/wBGSMQMbmvQdkTMD/WaMANCWmZPMAAAAASUVORK5CYII=" width="48" height="18" /></span><span class = "S2"> using the schemes below with </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="56.5" height="18" /></span><span class = "S2"> :</span></div><ol class = "S14"><li class = "S15"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="94" height="39" /></span></li><li class = "S15"><span style="vertical-align:-16px"><img 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src="data:image/png;base64,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" width="198" height="39" /></span></li></ol><div class = "S3"><span class = "S2">and compare the results with the exact solution. For each scheme, plot the dependence of the discretization error on </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="18.5" height="18" /></span><span class = "S2"> in logarithmic scale. Can you determine the order of accuracy of the scheme from the plot?</span></div><h2 class = "S5"><span class = "S2">Solution</span></h2><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">u    = @(x)    sin(pi*x);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">dudx = @(x) pi*cos(pi*x);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">x    = 0.4;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">minpow = -5;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">maxpow = -1;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">resol  = 20;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">dx = logspace( minpow, maxpow, resol );</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">dudx1= (            u(x+dx)-  u(x   )          ) ./     dx  ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">dudx2= (            u(x+dx)-  u(x-dx)          ) ./ ( 2*dx) ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">dudx3= (u(x-2*dx)-8*u(x-dx)+8*u(x+dx)-u(x+2*dx)) ./ (12*dx) ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">e1   = abs( dudx1 - dudx(x) ) ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">e2   = abs( dudx2 - dudx(x) ) ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">e3   = abs( dudx3 - dudx(x) ) ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">clf; </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">loglog( dx,e1,</span><span class = "S16">'.'</span><span class = "S8">, dx,e2,</span><span class = "S16">'.'</span><span class = "S8">, dx,e3,</span><span class = "S16">'.'</span><span class = "S8">, dx,dx.^1,</span><span class = "S16">'k-'</span><span class = "S8">, dx,dx.^2,</span><span class = "S16">'k-'</span><span class = "S8">, dx,dx.^4,</span><span class = "S16">'k-'</span><span class = "S16"> </span><span class = "S10">);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">xlabel(</span><span class = "S16">'$\Delta x$'</span><span class = "S8">, </span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S10">); </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">ylabel(</span><span class = "S16">'$\epsilon$'</span><span class = "S8">, </span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">legend(</span><span class = "S16">'(a)'</span><span class = "S8">,</span><span class = "S16">'(b)'</span><span class = "S8">,</span><span class = "S16">'(c)'</span><span class = "S8">, </span><span class = "S16">'Location'</span><span class = "S8">,</span><span class = "S16">'southeast'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">annotation(</span><span class = "S16">'textbox'</span><span class = "S8">,[.3 .06 .2 .2],</span><span class = "S16">'String'</span><span class = "S8">,</span><span class = "S16">'$\Delta x^4$'</span><span class = "S8">, </span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S8">,</span><span class = "S16">'FitBoxToText'</span><span class = "S8">,</span><span class = "S16">'on'</span><span class = "S8">,</span><span class = "S16">'EdgeColor'</span><span class = "S8">,</span><span class = "S16">'none'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">annotation(</span><span class = "S16">'textbox'</span><span class = "S8">,[.3 .38 .2 .2],</span><span class = "S16">'String'</span><span class = "S8">,</span><span class = "S16">'$\Delta x^2$'</span><span class = "S8">, </span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S8">,</span><span class = "S16">'FitBoxToText'</span><span class = "S8">,</span><span class = "S16">'on'</span><span class = "S8">,</span><span class = "S16">'EdgeColor'</span><span class = "S8">,</span><span class = "S16">'none'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">annotation(</span><span class = "S16">'textbox'</span><span class = "S8">,[.3 .55 .2 .2],</span><span class = "S16">'String'</span><span class = "S8">,</span><span class = "S16">'$\Delta x$  '</span><span class = "S8">, </span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S8">,</span><span class = "S16">'FitBoxToText'</span><span class = "S8">,</span><span class = "S16">'on'</span><span class = "S8">,</span><span class = "S16">'EdgeColor'</span><span class = "S8">,</span><span class = 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" style="width: 560px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"></div></div></div></div></div><div class = "S12"><span class = "S2">Note that the slope of error </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">&#949;</span><span class = "S2"> with </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="18.5" height="18" /></span><span class = "S2"> reveals the order of accuracy of the scheme.</span></div><div class = "S3"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">2.4) Steady heat conduction</span></h1><div class = "S3"><span class = "S2">The steady heat conduction in one dimension is governed by:</span></div><div class = "S4"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="93.5" height="42" /></span></div><div class = "S3"><span class = "S2">where </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">T</span><span class = "S2"> is temperature, </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">&#945;</span><span class = "S2"> is thermal diffusivity and </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">q</span><span class = "S2"> is internal heat generation. With finite differences we can discretize the equation as </span></div><div class = "S4"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="277" height="40" /></span></div><div class = "S3"><span class = "S2">Let us assume the case </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="119.5" height="20" /></span><span class = "S2"> with fixed temperature on boundaries</span></div><div class = "S4"><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="76.5" height="20" /></span></div><div class = "S3"><span class = "S2">We write the discrete problem in matrix-vector form</span></div><div class = "S4"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="57.5" height="30" /></span></div><div class = "S4"><span style="vertical-align:-52px"><img src="data:image/png;base64,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" width="359" height="115" /></span></div><div class = "S3"><span class = "S2">and solve it with MatLab. First we need an analytical solution</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S16">Ta(x)</span><span class = "S10">                                                 </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">F  = sin(2*pi*x);                                         </span><span class = "S17">% Source term</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">x1 = 0;     xN = 1;                                       </span><span class = "S17">% Boundaries of the domain</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">Ta = dsolve( -diff(Ta,2)==F, [Ta(x1)==0,Ta(xN)==0] )      </span><span class = "S17">% Analytical solution                      </span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="8974E6EC" data-testid="output_3" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Ta =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,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width="66.5" height="41" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">figure(1); clf; hold </span><span class = "S16">on</span><span class = "S8">;                                  </span><span class = "S17">% Clean the figure window</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">fplot( Ta, [x1,xN], </span><span class = "S16">'DisplayName'</span><span class = "S8">, </span><span class = "S16">'analytical' </span><span class = "S8">);        </span><span class = "S17">% Plot of the analytical solution</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">Ta = matlabFunction(Ta);                                  </span><span class = "S17">% Convert symbolics to function handles</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">F  = matlabFunction(F);                                   </span><span class = "S17">%     otherwise the evaluation takes too long</span></div></div></div><div class = "S12"><span class = "S2">in order to compute the discretization error</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">N  = [5,10,20,40];                                        </span><span class = "S17">% Number of grid points</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">eps= NaN(size(N));                                        </span><span class = "S17">% Numerical error</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S18">for </span><span class = "S10">k=1:length(N)                                </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    dx = (xN-x1) / (N(k)-1);                              </span><span class = "S17">% Grid spacing</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    x  = (x1:dx:xN)';                                     </span><span class = "S17">% Grid points</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    e  = ones(N(k),1);                                    </span><span class = "S17">% Auxiliary column vector of N ones</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    A  = spdiags([e -2*e e]/dx^2,[-1 0 1],N(k),N(k));     </span><span class = "S17">% Matrix of discrete second derivative</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    f  = F(x);                                            </span><span class = "S17">% Vector of right hand sides</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    </span><span class = "S8">A</span><span class = "S8">(1  ,:) = 0; </span><span class = "S8">A</span><span class = "S8">(1  ,1  ) = 1; f(1  ) = 0;             </span><span class = "S17">% homogeneous Dirichlet BC at x1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    </span><span class = "S8">A</span><span class = "S8">(end,:) = 0; </span><span class = "S8">A</span><span class = "S8">(end,end) = 1; f(end) = 0;             </span><span class = "S17">% homogeneous Dirichlet BC at xN</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    T = -A\f;                                             </span><span class = "S17">% solution T = A^-1 * f</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    plot(x, T,</span><span class = "S16">'.'</span><span class = "S8">,</span><span class = "S16">'DisplayName'</span><span class = "S8">,num2str(N(k),</span><span class = "S16">'%1.1e'</span><span class = "S8">));     </span><span class = "S17">% plot discrete solution</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    eps(k) = max( abs(T-Ta(x)) ) / max(Ta(x));            </span><span class = "S17">% discretization error</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S19">end</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">xlabel(</span><span class = "S16">'x'</span><span class = "S8">); ylabel(</span><span class = "S16">'T'</span><span class = "S8">); legend(</span><span class = "S16">'show'</span><span class = "S10">);</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsFigure" uid="DC80902C" data-testid="output_4" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="figureElement" style="cursor: default; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><img class="figureImage" 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" style="width: 560px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"></div></div></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">figure(2); clf; </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">loglog(N,eps,</span><span class = "S16">'-*'</span><span class = "S8">, N,0.01*ones(size(N)),</span><span class = "S16">'k--'</span><span class = "S8">, N,N.^(-2),</span><span class = "S16">'k-'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">xlabel(</span><span class = "S16">'$N$'</span><span class = "S8">,</span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S8">); ylabel(</span><span class = "S16">'$\epsilon$'</span><span class = "S8">,</span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">grid </span><span class = "S16">on</span><span class = "S10">;</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">legend({</span><span class = "S16">'Discretization error'</span><span class = "S8">,</span><span class = "S16">'$\epsilon=1\%$'</span><span class = "S8">,</span><span class = "S16">'$N^{-2}$'</span><span class = "S8">},</span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S10">)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsFigure" uid="C372F96C" data-testid="output_5" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="figureElement" style="cursor: default; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><img class="figureImage" 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" style="width: 560px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"></div></div></div></div></div><div class = "S12"><span class = "S2">From the second figure it is clear that we need at least 20 grid points to reduce the discretization error below 1%. We can also see from the slope of error decay that the scheme is 2nd order accurate.</span></div><div class = "S3"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><div class = "S3"><span class = "S2">Let us now replace the source term </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">Ta(x) </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">F  = @(x) ones(size(x));                                  </span><span class = "S17">% Source term</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">Ta = dsolve( -diff(Ta,2)==F, [Ta(x1)==0,Ta(xN)==0] )      </span><span class = "S17">% Analytical solution </span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="BC9F1374" data-testid="output_6" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Ta =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI8AAABOCAYAAAAZ10WCAAAKKElEQVR4Xu1de4xUZxX/nTvTHUJBgs/EB60abf+woYqKG5a538wuZKEkSi22Imi1alX6EJRApI1FTWxFbagNNUYbH8VXKzSKpVLZ+e7sJkDr+khttRqTWnxGrOiOy7LM3GPO5l5yO+7u3Hvn7uzs3G/+273f6/zO736Pc853LsH8DAIxEaCY9Uw1gwAMeQwJYiOQOvIsW7bsggULFtzIzKfL5fK9sZHrgIpKqYsBfAbALVrrp6OKlDbykG3bNwB4ZaVS2TE8PHwuKmCdVj6fz7+eiO4govdprf8URb5UkUcptQ7Almq1unFoaOhfUYDq4LL+C9U3Nja2+cSJE/8JK2tqyCNvmGVZ3wFwrdb6eFiA0lBu9erVF46Pj+9n5icdx9kFgMPInQryBMB5hoi2aa2rYcBJUxml1FuY+QeWZW0slUpOGNlTQR7btjcQ0T0A+rXWPwsDTNrKyEFi4cKFX2HmF+dyuXccOXLkv40w6Hjy9PT0LM5msweZ+Z9E9C6t9VgjUNL63LbtAhEdFJxKpdKPG+HQ8eSxbXs9Ed0P4Bqt9QONAEnz8+7u7ud3dXU9DOBkmBeto8mjlMoy89cAFJi5t1wu/z4N5FBKzXNd90rLsnYT0aZSqXQirNxKqdsBXEdEfaVS6VfT1eto8hSLxYtqtdoAgCcqlco1w8PDo2FBnKPlSCm1gpn3EdFlAE6FIUFQVqVUP4BDzLzNcZy7UkseHwgAn9da75yjhAg17J6entdms9l9ABSAjFcpMnny+fxriOgogOPz58/ffPjw4bNTDaCjZx6l1C0APg1gQ6fud1asWLEwm82KnDcS0QHXdfdZlvUBsWfFmXkC+54LiahXa/231JFnzZo1udHR0W/J8dyyrFVR1v1Qr3qbFPL9U9Vq9VNDQ0O/k2HZtn0TEe2NQx4fNyIqAujTWv8ydeTx3yAiWiJvUKlUeqJN9D3jw2iGPDI4pZTYxD5ERP2lUukns06eAKM3TLYeK6UuB/BTAC+Q58w80syM0dvb+5JaraalrUwmo44ePfr3qUBQSr0HwNf958x8s79ZVEotEMsrEa0O1L9Vay3e6Lb8NUse27a3EtEXgzhMJmhL9zxeOMQNRLRHdFo3ODkpbARwnzfQQwA2a61Px9FQoVBYysxCxlONyAOACoXCm13XPUBEL2Xmh4JWVtlEWpb1CICLmPkvAN7mOM5jccbVijoJkGdi2fNOXHfO+szjD0BsEMy8n4iuZOaBsbGx9b4nVyl1HYCvylGxGeJIXz55mPnRsOb2QP9C2FW+K0MpdSkzywlEfm1NnGb3PHX1v6y1/nDbkMdT7BXMLNZecRVMKEkp9XIAP2Lmk2NjY5uihAZMJlwc8hSLxZe5ritm+aUAdmqt7/B8PnuYeQMzryuXy79oxezRTB9JzTwA2o88y5cvf968efPEhyI7+ltlv+HtK35z5syZm5olTtyZx9ss7gBwOzOXXde9yrIssQ/1E9HVWutfh1WqePLPnj37fSJaG7ZOnNPRZG13NHk8JYkdQpaop5nZAvBIpVLZmpQVOM7M45HuEtd1jwBYTERy9M2JqT+qa8OQJ8IrE7XoypUrX2RZ1sNE9AZm3lOpVHYlGRYaccMcHL5E1klY5nZmfiyTyawfGBj4c1T5ZrN8UjNP222YPVDlZHW1OC2JaD6A73kRfomFS0Q5qgcV7Z2sDgB4HTM/Y1nW6lKp9NRskiFq3wmQp/2O6h4Ilm3bW4joE8z8OQAf9wh0/nQTFazJyvf19S06d+7cD4nokrBGQqXUGwE8IPsvAJd6+5WJjXMSY2pVG82Sp+2MhAKcd3LZJn4YZpY4m8cDx/Y9juPIZjVU/GwjRQTCMdaHMTbm8/m8ZVnfBrBHa/0lpdR7ZU/GzD93Xbd/cHDwH436bJfnzZCnLd0TnoFQTlYfJaKNWmux5YgpfMK6OxNLRFjHqG3bq4hIiLN/ZGRku+y9fO+yGA0BvF9rfd4C3S4kmWoczZAn4Bhd5LquGhwc/OtU/bTEwuwTx1uq7nUc53p/hgko6RXMvMtxnM8mNfsUCoVeZhbfzG1TuRN84jDzs0Gw6twpTrVaXT9Xrut4AV0yi48x81rHcUphCd9WIRlB4nguiW8S0fV+LLG/vBDRu5l5lJk3l8vlBwG4YQWeqlxPT8+STCYjboWnJgsGC8w4LwTwB9d11wSP5EqpqwBICKv87h4ZGZGLgu0YUEbd3d2Lc7ncfGZ+JxHJ9ZlFMmhZdoloRyaTebyrq+v0dPE53krQPsFgAe/2mwJKlrtT3/D/rlOSCHzeMdkMgYSYYiVl5kImkykODAz8Mdhe4A2d+Dcz3x8MgPIjEYnoVd7z5/i8mhlbknUDy1TDZht5yk0YagBC70bAQ56vzATAT0MvEwBfB47vCgFwOsyNgIavbgcXkBfNc0pvchznYCNRW7JhbjSImX5eKBTEESu3KNaZS3+To20u/U3BQgkD8YK9zoyMjHwwSTfITBO/Ve2b68bTIJ3P5y8jogeJaIvWWi62mZ+HgEl0EIIKXoqVnbVabcN0xq8QTXVSEZNiJaQ2TXKnOqBMcqeQzPGKWUqpj7iuO5r2tHLFYvHVruvurtVq2+PMxP932grEwYjVNdSvPmA8VCVTaM4jYMgz51U4ewKkws4ze/B2ds8tIY9S6jYAn+xsKFMjXUFrPXGZ0pAnNTpPTNDWkiexYZuG2gqBlsw8bSWxGUxiCBjyJAZl+hoy5EmfzhOT2JAnMSjT15AhT/p0npjEhjyJQZm+hgx5YupcwltzuZwiorcTkQ1AUsRIFtJ/M/MwEd2ptZbY6aZvgcQc4oxXM+SJCLF3n0vulkmGswsAOMy8O5vNPlmtVpcA2E5Efuq8vf4lwojdzInihjwR1RRMncLM93hf0TmfoMGPBfZS2dYkKVSYYPKIw2iL4oY8EdXgkwfA5V6e4t/WNxG47iOx09Nm14rYfVsVN+SZAXUEY6I6OdbJkGeGyWNmnhkAuJObrLs+/Zyr1Z0kt5l5EtZmXargR4noCq31qYS7aYvmDHkSVkOhUHgrM3+XmV2xAXXyHTFDngTJ431ERLLOX8zMWx3HuTupXEMJDjOxpgx5EoLSS6hwn5fH8GOSmq6TrcsCmyFPAuQJEoeZ91YqlZ1puA9vyNMkefzPCwC4GUBHuyPqoTLkaY48E9eXxQkqKVySzGDf3LBaU9uQpwmcJXECM0sC8qNJfGyliaHMSlVDnpiwewkCDhGRZFFdWy6XT9Y35aVpW0pEx/wEnjG7a8tqhjwx1OJvkAH0el/DmcgpXf9TSkk622tDfCwuxihmv4ohTwwdKKX8L/YcZ+YvAKhO0kyPxPzIN93Hx8f7jx079myMrtq6iiFPRPUEv9YTpqrxqodBKSVlAlnl/Q/fTyu5IU9KiGHEjIaAWbai4WVKBxAw5DF0iI2AIU9s6ExFQx7DgdgIGPLEhs5UNOQxHIiNwP8A+ZqBmpJSAJIAAAAASUVORK5CYII=" width="71.5" height="39" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">figure(1); clf; hold </span><span class = "S16">on</span><span class = "S8">;                                  </span><span class = "S17">% Clean the figure window</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">fplot( Ta, [x1,xN], </span><span class = "S16">'DisplayName'</span><span class = "S8">, </span><span class = "S16">'analytical' </span><span class = "S8">);        </span><span class = "S17">% Plot of the analytical solution</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">Ta = matlabFunction(Ta);                                  </span><span class = "S17">% Convert symbolics to function handles</span></div></div></div><div class = "S12"><span class = "S2">such that the analytical solution is a parabola. Then compute the discretization error as before</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">N  = [3,6,12];                                            </span><span class = "S17">% Number of grid points</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">eps= NaN(size(N));                                        </span><span class = "S17">% Numerical error</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S18">for </span><span class = "S10">k=1:length(N)                                </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    dx = (xN-x1) / (N(k)-1);                              </span><span class = "S17">% Grid spacing</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    x  = (x1:dx:xN)';                                     </span><span class = "S17">% Grid points</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    e  = ones(N(k),1);                                    </span><span class = "S17">% Auxiliary column vector of N ones</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    A  = spdiags([e -2*e e]/dx^2,[-1 0 1],N(k),N(k));     </span><span class = "S17">% Matrix of discrete second derivative</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    f  = F(x);                                            </span><span class = "S17">% Vector of right hand sides</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    </span><span class = "S8">A</span><span class = "S8">(1  ,:) = 0; </span><span class = "S8">A</span><span class = "S8">(1  ,1  ) = 1; f(1  ) = 0;             </span><span class = "S17">% homogeneous Dirichlet BC at x1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    </span><span class = "S8">A</span><span class = "S8">(end,:) = 0; </span><span class = "S8">A</span><span class = "S8">(end,end) = 1; f(end) = 0;             </span><span class = "S17">% homogeneous Dirichlet BC at xN</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    T = -A\f;                                             </span><span class = "S17">% solution T = A^-1 * f</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    plot(x, T,</span><span class = "S16">'.'</span><span class = "S8">,</span><span class = "S16">'DisplayName'</span><span class = "S8">,num2str(N(k),</span><span class = "S16">'%1.1e'</span><span class = "S8">));     </span><span class = "S17">% plot discrete solution</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">    eps(k) = max( abs(T-Ta(x)) ) / max(Ta(x));            </span><span class = "S17">% discretization error</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S19">end</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">xlabel(</span><span class = "S16">'x'</span><span class = "S8">); ylabel(</span><span class = "S16">'T'</span><span class = "S8">); legend(</span><span class = "S16">'show'</span><span class = "S10">);</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsFigure" uid="764DFB8B" data-testid="output_7" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="figureElement" style="cursor: default; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><img class="figureImage" 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" style="width: 560px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"></div></div></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">figure(2); clf; </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">loglog(N,eps,</span><span class = "S16">'-*'</span><span class = "S10">);</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">xlabel(</span><span class = "S16">'$N$'</span><span class = "S8">,</span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S8">); ylabel(</span><span class = "S16">'$\epsilon$'</span><span class = "S8">,</span><span class = "S16">'Interpreter'</span><span class = "S8">,</span><span class = "S16">'latex'</span><span class = "S10">);</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsFigure" uid="8B6C476B" data-testid="output_8" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="figureElement" style="cursor: default; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><img class="figureImage" 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" style="width: 560px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"></div></div></div></div></div><div class = "S12"><span class = "S2">Note that no matter how many grid points we take, the numerical solution always coincides with the analytical solution. Even with only 1 interior node, the discretization error drops below the double precision. One can show using Taylor expansion that the error of this discretization scheme scales with 3rd and higher derivatives of the solution, which are zero in this case.</span></div><div class = "S3"><span class = "S20">Important Note: </span><span class = "S2">Interpolating the numerical solution (e.g. for plotting purposes) linearly on a small number of grid points can create additional errors, although the numerical solution is exact in this case. Always interpolate numerical solutions on coarse grids with an interpolant of the same order as the discretization scheme!</span></div></div><div class = "S0"></div><div class = 'SectionBlock containment active'><h1 class = "S1"><span class = "S2">2.5) Friedrich's equation</span></h1><div class = "S4"><span style="vertical-align:-36px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZQAAACoCAYAAADHChjCAAAgAElEQVR4Xu2dBbA1SXmGHyTBCRIIgRAgQBGcBYIs7iEEDe6Lw+JkcSdIcIK7u1twlwAJUECwgmBVuEtg0aSeTXfSTObMmTl3Zs7I11W3/r/unTPd/XaffvvzoxEtEAgEAoFAIBDoAYGj9fCOeEUgEAgEAoFAIEAQSmyCQCAQCAQCgV4QCELpBcZ4SSAQCAQCgUAQSuyBQCAQCAQCgV4QCELpBcZ4SSAQCAQCgUAQSuyBQCAQCAQCgV4QCELpBcZ4SSAQCAQCgcDcCeXowFmAw4BLAIcAnweeAzwN+EEscSAQCAQCgcA4CMydUK4HPBm4C/AC4NfAdYEnJEK5F/DLcaCMXgKBQCAQWDcCSyCU8wF3LYjjBMATgdMncvnqupc4Zh8IBAKBwDgIzJ1Q6lA6DvAY4OxBKONsouglEAgEAgERmCqh3BJ4SrFErwBuBvy4xbL9KfA84BPALiqvkwLXAa4OXCz1p13mbsBrW/QfjwQCgUAgsEoEpkoojuscwHOBcwIPBe4D/HbLKh0z2VOuCtwA+ELHVb1osr18DHhYssk8AvD3lwU+1PF98XggEAgEAqtBYKqE4gIoKbwQuBxw/fT/poVxLkoWtwNuAny24yqeGXg28L0kDX0rfV7D/21mpj47ZcLr4gUGVwZetwETveXOD9wUuDRwGuCnwKuBOwI/7IhlPB4IBAIrRGDKhOKh9iLgdMAVgY82rI/z0G34HsBtk+twl+XMdhdVbarWnll8+A+B4yV12++6vHTPzzqnI4AHJElNFd4na8bk3B4MXAV4IPBm4ArAo4DnJ4nvyD3PJboPBAKBGSAwZUI5D/D6RA5KCd9owFNbx/2TJNFVMvG1ua+fJdtJ3cE7g+X8f0MUN92pJQlVgEpfZcsqQtV7/l2J8L+AP05k8tbk4DDHuceYA4FAYGQEpkwo+TB80pZbsqoqbSxKJ7uQiZDfCXg08MZ0sC5FxZPnpdfb3YFfVfaXtqGXAJ8Gbgh8M/3dfXHC9PwvRt6T0V0gEAjMFIGpEsoxgAclkrhzwy35ZICE83TA23RuqnvuC7wB+MCWtTlxUnFpyG9r/J/DcquqU/KQVG4FPLUy6PLvS5r3HNYmxhgILBKBfRNK1UXXVCnvAF6aDPHq9VVnvbcGfceuvcMUK3XtU8A1gc9t+LufvxpwB+AiNc88I/3t5zNd+ay2utAGD7VsozoUuHbCfKZTjWEHAoHAFBDYF6HYrweZEe3HTv/qUWTqFI3H3piNeP9gg3dVaUivw9I4lGs1GOiVggx+PCtwP+D4KW7ly+ll3z6ACm0Ka6vbtfE7392AoWT6yi0G+ynMI8YQCAQCM0FgX4Si1GGMia65h1c8uP4IUDqQWPQy8u+6sA7VtCO8B3g3sM34P9QYdn1vnbvvx4GXJVdfg0OrkpYuxaaq0Qh/kpqON0mEu44xPhcIBAIrQWAfhHKqRBTnTYdaNfq8lDwMZtSlVc+joVqOyt9m/B+q/13fqwR3z2Rsf3GyJemUcGrgH5Lrr++u2qBUhZ0tSS03T2shuRs0+puUYWBIAt91vvG5QCAQmDgCYxOK/WkkNsbB9CgGIf6kgpFGciUTYyGagvH6gFZ1m2MxcLHJ+N9HX32+w9iRh6dx6y7t/0tvrCsVaWKM8H9bpfPjAo9LNqg6g32fY413BQKBwEoQGJtQcp4to7E3Rb+fIbmy6ra6KRivr+UpI8rrDt6++unzPaUzwssBJayqm7OG+PcnaaPOjpTnbfxNpJTpc3XiXYHAihEYm1Auk9x7mzyw8jNjxITkgMbvbDHgT2mLmDlAFZeFxSTc0l06j1MSMb5kU1LNCxTrYP2YSPE/pRWOsQQCM0VgbELJgXZvSQbw71dw0/NKjyttJ5uC8fqE2mA+7Qddshn32f8u7zLflob2TdHvvtMgz4c0xNVku9EYTg+7zDE+EwjMCYFTJNf7Y9UM+lU7JKmdyty9eOaM6+WYzPpuBg4zi/xeG5tQJArzRRlkJ7lUo7DPlOIhzDB8o2RnGQrcMnhyLoF9uXiYHlrm6PKn6rBQPlMXX1IGNI7h9DDU+sV7A4GpIOC55eXMA9bQh7LpONOUh3Aqc6gbhzZs7ctl02nqP5PJoioQjFoPpfTeqiMU/65x2eSOehkNrdsvjf9Dk1dfm6YMRtxkgzKuRtvKiTYk1TS7gEk3tWMN7fTQ17zjPYHAlBGQUHSO8ez6f4fslAe+w9ga57ovCaWqajGeQl2+ebnOnfJIDa3bz4F/BjRuy2a8A+6DfKSU4C5ck1ZGqcsYE9Vdb0+YGthYtjxvfze008MgIMRLZ43AyVMGC7NgWL5bidoCdv+SbIPvq9FcTH3CuxDKpiwhT05xcUNmNlc154VSLZHerV2S4U6KUHLCR43AGo4/DDg5b9uHJHuGqePdYG0rNO662bJr7ZwCGrP3lnOuIxT/bsZgJZlNcTXZYL+JcHbFMz4XCDQhYGZr456MkfrXtD/9/tusxaNqxdpHOpmYDmlTyqQpotyVUHzec87LrGpnC/d5mbbCrJqZulCAPuatAOE5q6r8bxu8QJv6mhShnDYZczz4zNtlehRdWM3VZTZcD0kDHf29aiiZc4igRoHV+O/PnHJ2lRJK1c3ZgFETYn49bZi6uJrSbjSG00MfX4J4x/wRKMskeAO3nHY1eFZJ5R+BW6eL5mEzSn3UhVBUOavy1+DtRfqdxfJKKnpwakMuy0n0sQM8ez0f1EqItW1beqq6fidFKA7wXGliZvf1hmKAnZ4QplaXoc0ynFubSo27gF0arjWaaZSfQ8sJH/86ecGJl44NfwFYqvjxgFUaJco6+0iZ1iYCGuew4ssYo5cfPSm/tMU9v7wwGXDs/v7lDCDoQijZS/M5yeaigTu30stVDUJZUmJXGAyCvkVSb2k7NZzgGinLxiIIZVdg+vxc002/z358V1ZTbfJs69KfktXtgcemD5m3S88S3RZVEyg6m33ZW4ikIsmUnnR/mfJ8mRQzcnZ1QT6e3RUBnV/c+x5i26TiUoI2jZCfsVbP1FtbQilLZWy60OU4POfcR7C1mgszkpjX7ysJyGx6CELpaWdl+0lTNuOeuuqVUByT3nD5xqGkZcZgjfBulpIofbYa75M3q26MuhR/sa9JxnsCgQ0I5OBhs2S00ThkG5+vm0tZhbaEUmJRZwN1zuV3eCjtyd4I5c+T2GVeLXV+Ng3q3hq8Db8u6eHm9G3SCUD3ZG/6qtc0UJkYcajWp4RykDEq3WSVYgQ0/g+STZ42li8wMak6/7psBAdZiyE+W5d5OtcXUi//zzXqI9XOSg06cdiyFK2HUa4VpMFc1bQqGoOAu1bwzMHDvn/TIVriUTqeqPMvVeBD4NbHO9sSSibLpkwh7kkda3RQ6EOrUTe/0QnFw8fNZllcU5xrLFP/pnpFt9M7Ji+BucRvlKBeMjkGfC0Zvr7Qx45qeMdUCKW0n0wtEWYOeO2yFG0Op03va1uPx70xB9dq9eSSn2pPyUOV6H+kWj9HpO+qsUmqPiTKsqku1THFS6OegX7X9cQyI7UxFWcsCEeXdM+ELhewvLZtsSxv6LsGHFcl9Tb76iCHd1tCyRksmlRNpX13U0aRNvNpemZ0QimTOKpeccOV3la6nj0b0MA09ShQI8N1BHChPNz90hmb4bzqKkEedLGqn58Koejz/xrgRxPUTY9NKG3r8YyRT+6g+630oLIUtrEFpaG3JIwnpDilqpSR8ddg6/flWcCbACUVdfAWwtPJYxcVcX53W339kgmlDRZlAPhiCCUfgtvK6B70yzDG58uIeI3YepSZOl8JZYw2BULxBqtqwziAXW6ZY+A0Vh9d6vHsekMeay72Y10hPajUJKhVsIR2teXqnLrqXr4mIDYfdN+scWX1XdnmuEsGi/zutp/NgbdKRktSeZVE0USuiySUbDwy8KZuA475hZlTX2PftJuwMb5Hv3YJ1SBRdbK6aGtHKW+wc8L3oGNtU4+nVA22MSIfdEwH/XxOuNoUoLvN0Jv37SbbWhtj8qZ5HMSGsiSj/KoJpcyrpUHy3oC3eyv67dqGCFDcdSxdP6fLnQFX29qUCCUbALNhVjXGu2bi178N513/3qUej4Q89ZQ85SHVFKC7zdDbJWlrV9tVLpWgyrkNQWf9fluby657oc/PtbGhlElZVyehCLbeUAbQGc+gzSS3XX2j10AodZt0CiqvXb886ucPconYtd+hPtelHs8cUtNsI4qMY2norTM+D0koZTDuNhViGYcyJ0/ENoTiWnS1oQyFwehGed2Fza2jzl1DnFLKZ1I0u+lQzIcfrR0CfRGKyfOy63a7ng/+lOqUHER58LdtfsNYkl2XejybcqENiUPXd7cllG2ZvocklDIYt6mGj3MvA//aSDOb8Jqql1euQ6StapP0W9p8twWCdt0v+flRCeWiKdr6yORm+IHk7bHr4Nf+uSCU7TtgLELpcnDOITVNKXk03WZL4qk7pLrg0lXl5ernHH6mCDLL8Ec2bInsiWjySC+zVlLdpU2VUNpEwZdlyYfag6MRSqljHmoyu2yQOX+mL0LZBwZLUnltu6VX6/HMwRmlVBE1GeXLOjp13+uhCUUp5Top/YcSb10wcc5jZYybiRFNEjuX1lbllct3Gyy6KRYsO0A496FseKMRSunNsautZC6bYKxxzplQxsJorH42eTPtox5PX3MuXXo3uQ3nm/Gm/FhDEIqHrBHfxn2p5dB13QwVfh90GLFERdmyVGHsj3ZbbXdKLOam01OsS82OvrBt+562hFJm6Xh1iuP7YaWTrBarSx7ZdjzbnhuNUEpRsS7NtF+8syQg1DEPHWW+DZg5/D0IZTqrNKV6PH2hUiZfNB7FA0nPvtz+JKXwMDDREhFm8S0dLdqUcijPhbZJRbPqxgzDGuM9OP2dBGHKJsklR9znwnCSowHH3wDUlmjzMpX71PPOtSUU16SMG6pKYjlGStWge1UiriPdjMlLd9xE2ZaoLadJBVn3+k7p68uoW1/mLcLFNwWDelirfCk+m5rBjbHWeIYd1zE+tmcE2tbjMXeV9Tgs8jQH70SDAI2CV6tgipV/SrVEjEMyZ51Ze00g6k/1O1tG0uvOqmpKSSY3Ccf0My9Lv1CaeVgL77/SblNd9moEeJdn97yFarvvQijiqYRm9gGDPR8IKJVJoAZyStiHA5JFde+VxN7FacE+TwgcG/ibVI/Gd9mUlCR3hQPHYxmRptaJUHyRUoiTMu7iUikC14SQfsnUa+pOuauxbEqbIUtbHhyXSK7REqiipmRZ3vKmNO4Yy8EQmEI9noPNoP7TqpSUQiSEQ9P31v3s4W1KFb+/1bKy3oTd7xcpXul33RusB41NXb8VBHNRJn8naSkJVdU15chKm9VBCGUo19k+16ALodivB7ylJAw4Noean3etJBZrGuU089Ux7kooWTJvM+dtThedCaVNp0t4RpBV690lJYv8darB7k1PQplLcZ8lrEXMIRCYMwJdCWXXueZ6Rsb2DGWw3za2IJQNCEkoGv3MbZWrwmU3zNMncvG2NsdW5kNy/E1+73OcX4w5EJgSAmMRSpY02qodh8AoCKUDqllMt6LhdVPtlw4fn9SjGmvVjSpWN7mUTmrQMZhAYIYIjEEo2sPM8G4dqn3m45stoZQ+9nmPDRU5mt+f43A0Ti5B5bXNHXSG390YciAwOQTGIBQN+ScDLFGQNSr7AGK2hCJYGs71LNNw6GE/ZLBl9nDTl193vrm7RJfJ6KZWUGsfX4ToMxAYCgEPWStLWrK36qjQxnNqqHEd9L1qbI5beYmOHH+fUnPp/ft7TW+Dqbfs2eBEhopezpG8VrS7ScVtcur4bBpfmYY9glTnuoox7jkg0JTqZZvX1JTnt8k7bGPhrzkQSo7e//JAdg0x0G3Y8py3rYngnfKCN40tb3KD2KYeGDZXjGPcgUAgUCAwB0LJqSWG8kc35kY/e7MrlwFdc98oOd2G0dMa5iND9NxXNMYfCEwcgakTiuPTOJ71k6Zw6LPpOeE7lU7mSCbmBlK6Uk2Xg1Dfk6JsNeCZhC//GHVb5moTR432D04RuWUKjozxtvoVfa5FvCsQCARmjsDUCaVMz20UsGlg+moeuOYj02vCei+5aYgyBcIbanLp9NV3H+8xZYZuwebieW6ax9dT7iNTbJjR1FbFzVo3pubw99X6FLoamxLCaGtjcCQqqzzOIf1IH5jGOwKBQOAACEyFUDzkzCh6tZQCxcPMFC+mIrhb8jS4ZsqtVJ1uaXz2b9VD0vou3tpzMybDPDjmtDEivq59CtjU3wHg7u2jOeHfJVOaDAmlTPiXk79tKqOa604cHygz1OYCR+cOMultreJFgcBqENg3oegW/HfAI1J+MGslvAP4g+QirLrLts0OoFThIar6Rje90hvMPrSPmCPHpmufKVdMcGc+orrWVPN535tD92bVWM7DzLF18TLZO2NThbwyz5LqRN9nniclE+1JFjcqSXjfc47+A4FAYAYI7JNQyqI7700ZNstUJ2VRoDa6/LJ8aD4kTY9tP5KNh6+H8KP3HBh00G2RpYsfJe+tujoR2oRUezUFgmpzMQHgR5PEZoJA41WsX2G54WiBQCAQCHRCYJ+EYr4ps6AaOGN67H+rjLxMad02VXO+masuU4VmDqucssDDs1oLohNYE3g4V7XTmP7URJS/qIzLFNXOU6msKRC0rKPxAuAMyW1agokWCAQCgUBnBPZFKGXlMm/SuUJbOQEPOAnHojxtM2uWJYwN5vtaMlZby+EpLWo4dAZw5A+U9aZvBDyvpv/8jB5dYmDun01Nm9UrgfclNVe1it7I04vuAoFAYM4I7ItQzppqKvxZQ/T7BZL3lTdmJQ+ruG1rzseCQtpitB+cCHhG8oIqjdbb3jPVv5duv5sicLMqS8eCpgSXJ0l2JO0lqhrrpMSp4hDjCgQCgQkisC9CyXWTVU156H23Bpv8jK691iw5siV+pwNeDPiv5KJ0shS311xOeJPTQGlsl0i1h/y8BjdLjWpf+Q/AOjCq0Eq7U0uo47FAIBAIBP4PgX0QSpm0cJMdwOpzFrq6cTIUe/i1aXpAqQryeWNY7phiLpZCKNlGtIlQTLGiK7Rz1wGhLhBUZwdjTaxXrYOC9alfk9SDenmZ4iZaIBAIBAKdEdgHoZS3aAMIvRlXm7Ej2k+0iZgaRS+wbU27jDdyI8f9rIfppwvj/LbPz+HvWUKpiy85W/KUM7W1ONQFguba419MhcWsL17G8SyNgOewpjHGQGAxCOyDUErvrTpCMYJdycWAO+0nbRIbSlJWXjwkHaqqeZ6Z3mGcy6sWsmJlVlNdfB+X1HnnLVLU6NllneqqI0MmE0m6GrSZAyGNijd1vxH30QKBQCAQ6ITAPgillFCq8SVKGd6SVV1JKKpftiU2VD2mekdj9GFFTq58SL48BTBW6xR0AmoiD4uPwZvalGzZg8t1PBz4HvAi4NCEhe7AOiNkMtHry5xlumF/rJhTWTLYoE+DJZeA10SWLYYRCKwDgX0QSpnwUT2+dhJVMBLDEYBxFcakaLDfVqExk4mEUnWjzR5RphfRg6nM1zXn1dU7S0JREjErgKShpKJjgyqxNyUbinPMNiozD7+2mHQ180CZM83HNtY7mDNwMfZAIBAYFoF9EIozUkXjoaaBWJdVCcW4E2smm/DQw1KDsbm8vHmXEfQZkZJM/J2fMdGjKURs5SH5YeAWgK60SzHQD7sz4u2BQCAQCHREYF+EkotamTfKlB/m7zK31jsB1TpKJmWerbqYizI1i9M2Kr5qN8iuxxmWOVdP67i08XggEAgEAuMisC9CGXeW0VsgEAgEAoHA4AgEoQwOcXQQCAQCgcA6EAhCWcc6xywDgUAgEBgcgSCUwSGODgKBQCAQWAcCQSjrWOeYZSAQCAQCgyMQhDI4xNFBIBAIBALrQCAIZR3rHLMMBAKBQGBwBIJQBoc4OggEAoFAYB0IBKGsY51jloFAIBAIDI5AEMrgEEcHgUAgEAisA4EglHWsc8wyEAgEAoHBEQhCGRzi6CAQCAQCgXUgEISyjnWOWQYCgUAgMDgCQSiDQxwdBAKBQCCwDgSCUNaxzjHLQCAQCAQGRyAIZXCIo4NAIBAIBNaBQBDKOtY5ZhkIBAKBwOAIBKEMDnF0EAgEAoHAOhAIQlnHOscsA4FAIBAYHIEglMEhjg4CgUAgEFgHAkEo61jnmGUgEAgEAoMjEIQyOMTRQSAQCAQC60AgCGUd6xyzDAQCgUBgcASCUAaHeDYdnBS4DnB14GJp1J8H7ga8djaziIEGAoHA3hAIQtkb9JPq+KLA04CPAQ8Dfg08AvD3lwU+NKnR9jMY9/5fAjcDrgCcCZBA3wg8HvhKP93EW2aIwNGB8wM3BS4NnAb4OPAy4JnAd2c4p1GGHIQyCsyT7uTMwLOB76XD9VtptNcDbgNcF/jqpGfQfXDu+2sBTwTekkj024lY7pted2vgzcB/dX99fGLGCBwTuBNwH+AZwJOAIwG/D/cCPgMcDnx0xnMcbOhBKINBO4sXHwd4DHDLRCbevnL7Q+B4wI+B381iNu0HeSHghcC/V0jU74MHx/OBTyQV4Gfbv3aWT54gEes5Eskqpa25XTtJ6y9JxPKfCQyJ5u7Ag5IUq2SbL19rxuv35h6Esu6tcB7g9cDPku3kkyuAQ5J8AnDjGhJ1+n8KPC+pOjw8HgD8dsG4nAx4EeC/Sm1rJpS89qq7rgq8o7LuZwVeDijVSyjlBWzBW6T91IJQ2mO1xCcV7R+dblw3AH64xElW5nQ+4DUNJHqMdAu9B/DuJLF8Y8G4KJm8Avh5EApXA17ZsO5ZmvO7ohSr6uunC94bnacWhNIZssV84MTphuVN7KFJZ7zkm3heuEyi2k5Ub32/ZkX9/QvSYbFUpwSnXapxVPGtWUJRxatDivvjqenfX9TsDW0rD0w2FNVjX1zMidDDRIJQegBxZq9wzb2J3QG4SM3YNUT6N2+sS2vHBh6VnA2a5qmN5f1p8tdP9papY6Fn0mmBKwGXAg4FTpJUWM9JdoEfFJM4Q1rnGwHevOtaE+nm5+2vdCsv8Tou8LikHsrP3yod2FPD0wuWUocef6o5/alzyMiXDcd/YeADU5vIPscThLJP9PfTtyqdswPqg+8HHD95r3w5DUdvp7EN0fnW1wWRXb7M5aHRdAvNaqAzAnp9aUuZcvNioAeSJOK8/FEVcwng/sklWrvRXYF869YV9nTJHqAn0xfSIfr1YqJ6N+ku+8uGyXuGuJ90O9f2UMXVfjyoHeOHE7noDNGmlU4jbZ73mV0lLQlWQ7x2xaY1vwzw1pldNtpid+DnglAODOFsX2CMyXsmYicYi1AM3tS763Jb1BrGpLwUOOdMCCXjp/QlsZQEkO0C3wSuWOPumqWxXQ/i/AXI/XgZuQbw6fQHSevF6f8astuSiR8Zk1DarvkcpdfRDqkglNGgnlxHugo/JfnZ3yX52k9ukD0PqDw0miSUtodLz8Pb+XUSyhHA5WtUMOVcrgy8rtJLX4RycuDpSeWWPaC00bi3tNMdtgfJtwugJVE0SShBKFvE1S6gx7PLQKC0Jdw5xaIsY2bNs1gqoTTNupTK6uxBfRGKYzCyXNuUKi7tcBLLJYHbJ5XalPdYEEoPqxMSSg8gzvAVp0yqn4un1Cpvm+Ecdhmy+nxjLrKtQY+eOk+euUkoUyEUnQL0jlNa+RRwrORaO4dMCzkmy1iUkFB2+XYBQSg7Ajfzj+Uvz3dW5iq6iw1lql5JdVtQm8O5AW/bF0w5qA4pHhxaQvE8kaS15RjbYpyGe2wOre0lopRkdClfy2Ws1RoGobSCaXEP3RB4bvrSq5Ywvco+21hG+TIwzQNv09wvkDx5fL7O7rBPrDYRyS3SYf6TJCV8JMVIqN7UVqYr8dCEogRofjRdb3Wntb+DJNkc0yhfSu2mIzLNyq9qwDZWR2+wTU4OU9sbo44nCGVUuCfRWRkJPpWAxrEIpW0UfHYN1ZXWdP5TTknjoftw4LZJMjB+oozebmtDUUV1TeBzO+5S3dCfnFL5nH5Dfriurx6TUNpGwWdnljVkUei6XqHy6ozY/D9QxmIY1GbeqjW1bW60YpGj6ZukmKlgpgrmTcCXNqgvc64u07A3SSjOZ5fYHj+nCtU4F6UTbVRXSSlMXp0M9XNI6VOq6z64Ict2GU3fJMVMZW+MPo6QUEaHfO8d5qA9Axrr4hL2PsCBB5DjIgzC06XVg6GMiC5vqnNIAJgjt9+eDsFqrQ71/BKj86ojlDKIcxf1nrYaJRNjTbSd/CbZbiQWAx7NezWXAm05z5uG+b8DXlXZi1ktJoHWJY8ceOtO//VBKNNfo75HmFNlrFVkd8/rxvrYDXr+fAB7QKvemHoxpayeU6cvYbyz2DBnS/M8RcqMUEcope1A24DYOGc9tLS7mIJGu0xdy2Ti89bNyViVN3kl4Ns1vKPv/X2Q9znnB6eLhlmFXf8sXblvvGCYEaCadeAgfS7qs0Eoi1rOrZNxvU234s+Sc3ZtA8IU9h4cxkqYRsP/G+FtepCHpGJjxlTMIZW7Ki2DNL0xm6vLg9A0Okb5O0/tUxZK83B8JHDvSiS9diVjkbTD2HTx1XZ06mQ7kgxMx1NtmUzs512pHMDXiofKFCVG7ysJ1rlob1ursf/+J6lip9H+Sl0mjHT+4us+MaX9JkzGHuvk+gtCmdySDDqgUp1zz5RleNAOJ/xyb6PmurpJuombSNFUNKZc8VadCytNeAr/OzRJRXJUAtHTykPvWUnVZHG0XETND2TJS5tLbhq/b56IR/dZP68a6w0NebyynSm/o2pTKCUfn2nKTDA1jCVi1X+q67RR2fRa8xLWhMnU5jH6eIJQRod8rx2WvvbhQ7/XpYjOA4HlIRCEsrw1bZpRtp9s8mJZFxox20AgEOgVgSCUXuGc9Onm4+QAAAhdSURBVMtU8agn1+i6htK2k16MGFwgsEQEglCWuKr1czJJn3mWNJyqG9bwGi0QCAQCgd4QCELpDcrJvUjXzXOl+AMNixptdes0Rcd7JzfaGFAgEAjMHoEglNkv4cYJlBHxVt0zSEvvpdK1c7mzj5kFAoHA6AgEoYwOeXQYCAQCgcAyEQhCWea6xqwCgUAgEBgdgSCU0SGPDgOBQCAQWCYCQSjLXNeYVSAQCAQCoyMQhDI65NFhIBAIBALLRCAIZZnrGrMKBAKBQGB0BIJQRoc8OgwEAoFAYJkIBKEsc11jVoFAIBAIjI5AEMrokEeHgUAgEAgsE4EglGWua8wqEAgEAoHREQhCGR3y6DAQCAQCgWUiEISyzHWNWQUCgUAgMDoCQSijQx4dBgKBQCCwTASCUJa5rjGrQCAQCARGRyAIZXTIo8NAIBAIBJaJQBDKMtd1l1mdFLgOcHXgYukFnwfuBrx2lxfGZwKBQGBdCAShrGu9N832osDTgI8BDwN+DTwC8PeXBT60cJiOBVwauBNwZ+CTC59vTK89AscDrglcBbg18I32H13fk0Eo61vz6ozPDDwb+B5wM+Bb6YHrAbcBrgt8daEwuf8PAR4A/C3wCeBagJJZtHUjcHTgksBDgL8C3gL4nfj+umFpnn0Qyrp3x3GAxwC3TGTyzAIOa9J7O/sx8LsFwnRa4L5JxXeCNL81EopzfyJwjiDTo3ZBvmTcG7hqse+DUFocAkEoLUBa8CPnAV4P/CwdrGtQ9UiSt0jqrRcBLwGuAdxzpRLKyQBx8N+1S2dicJe0H54KvDntkxuHhNLuFAxCaYfTUp/SZvBo4I3ADYAfLnWixbxOBdwOeArwlUK994KVEoqSySuAnwehHCWlaSt5MvDdtDfuAzwwCKXdyRCE0g6nJT51YkAVl2L9QwG/OL9d4kRbzEnd+BoJ5ZjA3YEHrZRMW2yNo74XQShtkEr6wpaPxmMLQcBLxNWAOwAXqZnTM9LfvLGupS2BUDQiaxe6EnAp4FDgJMnB4DnJi+8HxYKeIa3zjYBsQ6qudxu7gf2VbuXXB16YXnRc4HHJPpfffStAddJcWhBKh5UKCaUDWAt59BjA2YGzAvcDjg/cC/hymt+3gc+OPNf8pe3S7YWBD3T5QMOzcycULwauoSTiYe3PT4FLAPcHzgQ8Abgr8IuEw2mA0wF6+T0J+ELydvt6gdORwMeBXzZg5xniftLt/Pypb1WpZT/PT5eXDydy+feW61Y6jbT8SO+eekEobZEPCaUDUst71BiT9wDvTu6Q+/SvD0I52P7K+D0qEUtJAEqjrwS+CVwR+GilqwsB7+9B5ZX78TKik8OnUz+S1ovT/3VLb0smfiQI5WD7YvRPh4QyOuST6VBXYQ3T3k71bPE2utY2dwlFQjkCuHyN1KZ08lLgnMCVgdcNRCgnB56eVG4Sh/Y5bTTuLe10h+1B8u1jP4eE0gHFIJQOYC3o0WMD3mYNXDQy3FiUNbe5E0rT2plSR5vG5YDSvpE/05eE4vtuCmiDU8WljU5iMTjw9kmlNsc9FoTSYdWCUDqAtaBHT5kOmYun1CpvW9DcdplKEEo/WQJ0CtBbTmnlU4ApbQ6feaaFIJQO36gglA5gLejRHND4nYg9OGpVl0Io2hzODSh1XBDQ8G5qmdyGllA8TzTIK/0a2yKZuMfm3IJQOqxeEEoHsBb06A2B56YvvWoJ06vss4VR/mDoSyQ5+v8nSUr4CPBFQPWmtjJdiYcmFAnMNC5XSLYc+8vBo7vMMIzyu6C2x88EoewR/D11rduwgWz3mFBAYxDK7pvBQ/fhwG2TZGCiS12Gc2trQ1FFZVbdz+04FN3QjTA3lc/pN+SH6/rqIJSuiO35+SCUPS/AHro3Ql6jqbdIg9qet4cxTK3LOau8VG+9CfjSBvVlztVlev4mCcU12TW2RxWqcS5KJ+YFM32JrsqvTob6Oaf0CZVXh29rEEoHsBbyaM7dZEBjXVzCQqbZaRpzJpQ89renUgM5B1UGwHo22jOMhq8jlLwfzrjBrXgbkNpqlEyMNdF28ptku5FYDHg0R9ycC7QFoWzbAcXfg1A6gLWQR3OqjCkENE4F0pwk0+A/b9faH+bSLgO8NQUuShjvLAZ+NuCxwClSZoQ6Qik9/sy8rIuvpKSHlnYXgx61y9S1TCY+b92cTGaWPrBQm7gqAZuMc9M7poxzOQ+j/K1omjNKTHncextbEMreoN9Lx6636Vb8WWPOrgy6OJwwGaz/JpU5NgDQpppGm4SpSLRF/GovK9W+U1VaploxeNBcXS9Ph56BjKbq94ZtvJGBrI8ErPNRRtJrUzMWyTnbLKbm3E+dKldKBqbjqbZMJvbzLsAU718rHspE569MC2OsU07H0n524z9pTrQ/SthJICbPNCeazfQyjwdMT+PeUBqLViAQhLKu7ZCLKamGsP6HWYbX2LKaqM3cd7UrtHl3X89IKgYSKoHoafUO4FlJ1WRxtFxEzf5UjUku2lxy0/h980Q8EqufV431hoY8Xlmqy++wDw/fTMCl5OMzkl6Z46uvuff9nrYOImssxrYV6yCUrRAt6oEyDYe69bUHNC5qcWMygcC+EQhC2fcKjNt/tp98cOG14sdFNXoLBAKBoxAIQlnPRtDIqp5co6txKMYrrLWg1npWPWYaCIyIQBDKiGDvuSuT9JlnScOpNhQNr9ECgUAgEOgNgSCU3qCc3It0eTxXij8w+E2jrW6dpuh47+RGGwMKBAKB2SMQhDL7Jdw4gTIi3qp7r0oxAaVr53JnHzMLBAKB0REIQhkd8ugwEAgEAoFlIhCEssx1jVkFAoFAIDA6AkEoo0MeHQYCgUAgsEwE/htyEZ0weLa1DQAAAABJRU5ErkJggg==" width="202" height="84" /></span></div><h2 class = "S5"><span class = "S2">a) Assume that </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">f</span><span class = "S2"> is a passive scalar. Explain the physical meaning of each term.</span></h2><div class = "S3"><span class = "S2">Friedrich's equation is equivalent to a classical convection-diffusion problem</span></div><div class = "S4"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="87" height="18" /></span></div><ul class = "S14"><li class = "S15"><span class = "S0">diffusion: </span><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="38.5" height="40" /></span></li><li class = "S15"><span class = "S0">convection: -</span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="17.5" height="36" /></span></li><li class = "S15"><span class = "S0">generation: -</span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">a</span></li></ul><h2 class = "S5"><span class = "S2">b) Discretize the equation using finite differences on a uniform grid</span></h2><div class = "S3"><span class = "S2">Common choice for finite differences are second-order centered schemes. Matrix representation of the discrete second derivative was given in the exercise 2.4) as</span></div><div class = "S4"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="123.5" height="40" /></span></div><div class = "S4"><span style="vertical-align:-46px"><img 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p0KmT1JOh3dnRkBI9AVAtlr2YTfFfTT6Sd7kkxHNUtqBGaFQPZaNuHPan78TVnd1rxvUFsFNvaeHwTW2AhUgYCyqz4oaKKb2Mqyuuljwl+FUH1/L+XiVX3IWiMjMCwC2WvZhD+sgTSabpbeK+ys9wd+OLAI2ZNkYPk8nBEwAmkIZK9lE34asF20UiqB2wIHA7sAuvGqnBvndNF5Rh/ZkySjbzc1AkZgOASy17IJv3/jCOOdgWcC+0TDmfD7x94jGIGaETDhF2bdK4R858p2eBRwEqCMkDpoMeEXZiyLYwQmhoAJvzCD7RB89a8GfhpkGzvve/YkKQxTi2MEjMDfEchey3bpDD91xib8UrJlDo+8RzQCdSHgbJkTsOfYhJ99WWMCmFpEIzBHBLLXsnf4w08TE/7wmHtEI1AjAib8CVjVhD8BI1lEIzABBEz4EzCSCX8CRrKIRmACCJjwJ2AkE/4EjGQRjcAEEDDhT8BIJvwJGMkiGoEJIGDCn4CRTPgTMJJFNAITQMCEPwEjmfAnYCSLaAQmgIAJfwJGGpvwnQ9/ApPEIhqBBAScDz8BpLGbjE342dexxwbM4xsBI7AUgey1vOzilVL2vjkB4NOB7wCnAB8Azgb+mvDe3JuY8Oc+A6y/EegGgU4I/0KhBN4RwKUiufQj8NXw79sBdwL0v3p+BbwOeDHw4250qbKXrYBDQsbMzwL7AmcNrGn2JBlYPg9nBIxAGgLZa3mj1ApK6/tW4PbRuPcP9VCb/6TKTU8GnhL9MIjEHgN8Pk3eWbRS4ZPLhEpXIvgDgW2C5kcDhwM/CD+a5w2ASPYkGUAmD2EEjEA+AtlreSPCv1wg9903IXz9SV8DIrDnR+0+BuwXSCxfhfreiI2ymXZfAu4NfKNnCLInSc/yuHsjYATaIZC9ltclfIl5VeBNwG0imQ8CDgX+3E4Pv9UjAtmTpEdZ3LURMALtEchey10Qvvp4xsIu/+OhXuvQBbrbQzefN50Pfz62tqZ1I9BZPvxUl04D527AyQvY3hr4RN14T1K77Msak9TSQhuB+hHIXstd7PAF63WBtwM3iDBePOTtGv6LAS8DHpnR8VB+8gyRBm+aPUkGl9ADGgEjkIJA9lruivCvDRwH3DCS8lkLbp4UBXLamPBz0PpH2+xJ0m4Yv2UEjEDPCGSv5a4If5kLqG/C7xnLarvPniTVImHFjMC0Echey10R/lVCGOeuA+7wp22q8aTPniTjieqRjYAR2ASB7LXcFeFfBzge2DES7oHAsRM3l84mzpyIDvsAOrVf9WRPklUd+u9GwAiMgkD2Wu6K8OW7PxHYNlL7DsCHR4Ghu0FrJHxny+xufrgnIzAmAp1ly8wNy7wrcEKk+bJomEsDe4b8MTcDLgzoF+rlIXwzN/GaD23bTbXsyxrthvFbRsAI9IxA9lruYod/kXCr9vGRcm8AHgv8Jvy35gdEuWKeBHwLuBrwSmAn4B7A5zLBMeFnAhaaZ0+SdsP4LSNgBHpGIHstd0H4O4SQzOsF5ZQ5UwQeX8QS4f8n8ELgjAiE5sKWkrAppt5P/whkT5L+RapqhJsDnwoaLUaqxWddR4XNz+8WNkXKX6Xb0EpTfk5VyFiZrhHIXsvrEv6VAE3cvSJNlEztJUBK5sdmcZjwu54KG/eXPUmGE62KkUz4VZhxEkpkr+W26ZHlTtklpEaWX755XhHy6jSunFWoPRSQ0G1cOqv69t+XI5A9SQxkFgIm/Cy43HgNBLLX8jLCV8pjhfipoElcAGUzub4CvAh4N/CHRAXkAtIp87uAlzqzZiJq6zfLniTrD+kejIAR6AGB7LXctsShcrbr4FUFT+Rv/CLwxwyFGlfQZzLcPxndV9e0ywgnZ8usbnpYoZki0Fm2zD7x01eDyvypHq4OalN8/X3KU3rfXUc4ZV/WKB0gy2cEZopA9lreyIffF34qi6jCKN/zzj4Z4q4jnLInSbKkbmgEjMCQCGSv5SEJX2cDBwQ0UqN4hgRvamO1jXDKniRTA8byGoGZIJC9lock/PsAijF+AvB/wSAaX2kZ7huie5qY5JnYay0120Y4ZU+StaT0y0bACPSFQPZaHorwl9W9jUF4LqB/ctMr9AVkar9bh2gmRTU9KtxJSH13nXbrRDhlT5J1BPW7RsAI9IZA9loeivDj2ORl2k81d/7tgPeE8FUVcn8MoJvGfT7rRjhlT5I+lXHfRsAItEYgey0PRfitNSr4xcUcQt8MF8i+3KPMXUQ4ZU+SHvVx10bACLRHIHstm/Dbg93kRfk68K+hFkCfbp2uIpyyJ0l7iPymETACPSKQvZZN+O2toUPT54cDZx1Iq5j6YpbQ9r1v+WaXEU7Oh9+VVdyPERgXgc7y4Y+rRvmjN4e1vwxpoPcG3hyqY90T+FrHKnQZ4ZR9HbtjXdydETAC3SCQvZa9w28HfHNY+6CQP+j6wDsARc88LETuLOt5sVDM/UMtYLW9OKDkc3q/eeQiej+gA+HbbCBqboRT9iRpB5HfMgJGoGcEsteyCT/fIs1h7U1C9a6zAPnXjwD0A7CY5zweQXjfADga0PuLbbcL5H7LkKdI5H+ZKL/6MmlzI5yyJ0k+RH7DCBiBARDIXssm/HyrNLv5d4a7A38OXciH/xpgWXnHxVHuFrKEqkB67AK6JvC20Fhk/9V88Va+kT1JVvboBkbACIyBQPZaNuHnm0nE/mxAfvu4epcqf+lHYHsgdtUsG+GKwGsBuXgaF1BzMKtLXA8O5wH50q1+I3uSrO7SLYyAERgBgey1bMLPs1JzWKu3FKVzbvS6YuSPBPZb4dZpXtH7xwQXjtJNiPhvC6g2sGL6+3qyJ0lfgrhfI2AE1kIgey2b8PPwbg5rVYhdBWIWH/13FXNJcetcI0T2aLevAjI6G9BN3e/miZTd2vnwsyHzC0agSAQmkQ+/SOQShFp2WLv4mhLBnQhsC9w9RPBs1LV+bPUDocyhcgWJ7H+SIMe6TbIva6w7oN83AkagFwSy17J3+Ol2aA5rPww8dYNSjoqokZtGNXpfuUk7jaqIHLmA7gx8Ovj9VRSm7yd7kvQtkPs3AkagFQLZa9mEn4Zzsxt/Tqj3K6CXPfGuXeUf9wUUtrn46Mfj1eFr4J/DLd3N4vfTpExrlT1J0rp1KyNgBAZGIHstm/DTLLTZYe1iDzcG5FuTW2cv4H0LDeT2Ucy+dvdvDdE+KuSurJuLB8Fp0uW1yp4ked27tREwAgMhkL2WTfhplmkOa7XDVx3ezfL2Xz5E3uwR2h4YFXj/97CzV6x9U/VLrh0Rvy5kKcLnhDSRWrfKniStR/KLiwjoHOj24ezmyUCfmVVLQV8co5Teu4YCSDsCOwfhTgdOCQEQQ7gzu8Tk6sDjwtrW5cfmPk6XY6zqK3stm/BXQfr36BnV4VU+m4OAb69+5W/E/RDgtJBcTZE3Ddn/NPw3/a+erUJRdx3gHhsmUVMRLGGo7CbZkyR7BL+wiIDWmUhOaTD2TIziqgHFq4SotXsDPwcOA44Hfg3o3orOwu4QItMeCJw6AaV1q/4RwDOBbYDcm+5dqpi9lk34q+GP8+Ssbn3+FnLriNzls9fu5mMhBYMKuTfPbsDJ4V+eEb4M+ir36GyZbazY/h2F34oUdJCvuxp6UsJ2249YzptNCnGFHj8AEEHFX8dxJTzt9NXmR+WIv4Uk2vjphvzTw9d488cxCd/ZMnuYLPcL8fJtu9aE0I5G8fnNI7dQ7OrRTkhErM9ePZvl42krR/Ne9mWNdQec6fvNTlBfbnLZHRfSaOgrcW6Er537ssi2OMhB0+QWIWKtpCkTf50pCk9rVxcuXx42cGMSfvZa9g6/pKk1jCzZk2QYsaobRbtX+XiVX6nxTzebh7kQfopR4w3VqpQkKf113UYcKbnko1dwxR+Ay4UN2u4ju3Sy17IJv+vpUX5/2ZOkfJUmI6EJ//ymigm/xB3+ssllwp/MkrOgJvzx5oAJf0vsLxiqxskvHgc4jGehtJFN+Gk4uVUBCJjwxzOCCX9L7Jt04KoN8cRwO32zkOfxLLflyCb8UixhOVYiYMJfCVFvDUz4/4BW6cAVuKC60Lp0qLTjTahybwboqGMTfkdAupv+ETDh94/xRiOY8P+BjOLvlTTw6z3Xf+jD2ib8PlB1n70gYMLvBdakTqdE+DdfUVpzmcKpIYqq/awYcj19VXZLMkjLRib8lsD5teER0Ce0bgnqeQGgHwA/wyBgwoeG7C8bbqx+YhjoOx2lFMLPXssOy+x0Hkyis+zr2JPQahpCTonw+0BUOXV0qXAnYCqpFJbhUArhZ69lE34f07rsPrMnSdnqTEq6ORO+bh4rJ5XqP+wPnLQiCWHJhjXhl2wdy7YFAib88SbEXAlfETkHAMoT9ShA2WKnEH650Uwx4Y+3hjxyJgIm/EzAOmw+R8KXF0GFgJRiQjv8Q4DzlmB6rVDX+cwO8e6rKxN+X8i6384RMOF3Dmlyh3Mk/OaQ9sch1v7sJWjJ3aOiQP8b4vKTAR2poQl/JOA9bD4CYxL+Zomy4jDAxfC+Js2u0kv3mUk0H828N5Q5U1lTlQJ4b+CMvNcn11ophV8Y3DlP20DfC4eyofLrqyiMslGW/jRFi26WULu6T13itaz00kqzvunjQ9tVCNX3d5VWfHRQ6+PAHYHfD6Tm3Ahf6+vSwEWBOwEiPf146dHtUrk4vgn8KqqKNpApBhkmLveZMmCJ2TIbuVWoSPUMlAVV5xHK3a9HhV20QVGlOtlRxYuGOJ/QnFIxmbsGOV4UCjSZ8FNm2ozaxKQ79G55boSfU0thKpkic5aKkqIdnPFCqYQfu3BWqTPUmrpY+BpSSgo9Sdh5h7/KfPX9fUzCrw9Na2QExkHAhD8O7pMb1YQ/OZNZYCNwPgQWCV+lVN+3Cifv8FchVN/f48NRJa9SLpNf1qemNTICVSOgcovHhFrJUjTJJWjCr3pOLFUuJvwPAdrxnzM/GKyxEZg0AovnCib8SZuzP+F3CGlptwdM+P3h7J6NQJ8IxISfXCPZO/w+TVJm33FMe/JEKVMVS2UEZovAtYHjgBsCyevYhD+/+XIF4K3A7XMmyvxgssZGoGgE4o1b8pe6Cb9om/YiXPwpqIsiqjx0ei8juVMjYAT6QkA7+xOBbYEPAPsB564azIS/CqH6/r4YzpV02FMfDNbICEwagTj4Ivmylwl/0jZvJfwFQ4Iq3YLUk3RDr9VIfskIGIG+ELh38OGr/+eGf1amdDDh92WOsvttknhJSuUn1w7BjxEwAtNBQLl83hjETU46Z8KfjoG7lDTeHaQWnu5yfPdlBIzAegioFvXzQhf3CYnUVvZowl8JUZUNWvn/qkTCShmB6SGgTJkvibLeJp/DmfCnZ+wuJI5DupxeoQtE3YcRGA6BOK1Ccgy+xDPhD2ekkkaKQzOVE1/pFX5YkoCWxQgYgQ0RuArwFmDX3NvyJvx5zqo4NFMFOO4BfHmeUFhrIzA5BOL0KK8KBVmSihiZ8Cdn684EjotT3Br4RGc9uyMjYAT6ROBWwKlhgIMAVbtKekz4STBV2Uil0VSWTY9DM6s0sZWqFAFVuXpN0C0pD36Dgwm/0hmRoFb8WagdgsK8/pzwnpsYASMwHgLxxclsd6wJfzzDjT1ynETNkTpjW8PjG4E0BOIInZNCDp2fpb3qKJ1UnGpstxVwCKBbt58HdHnjWzUqap2MQEUIxGmRXwYcCPwxVT/v8FORqrNdfD3bB7d12tha1YVAfGCbnQfLhF/XZMjVJk6x6oPbXPTS2muNXTfUDr4zoEtv3wgpbQ8HvpPWzWRaNfpq53najPI0XQLYJaQb183XnYBLBVt/BngD8EngL2tasjmwzfbfa1wT/proT/z1ywNvAvYIC1Pund9NXKeSxNf6Ut6iI8MFGbnQzgZE/MphpGd/QL7YlZkOS1JsA1l0LnRAuPIvssvegU5Ax0UR5Rp9IvA0YBvg2GDvb4dc9Q8JblO9px9BpUQ4r6WecUqFVuduJvyWyJmbo1gAAAXJSURBVFfyWnzi7xu33RtVOYt0I/KrYYf/4zCE1p1uN+vHVlfj9wXO7H74wXrU7vYRwBOA7aJR50D48SVG/YgfCvwhwuBCIXWx4uVVcGgf4CMtLRPfsFVU3QtzNwom/JbIV/TabsDJYTLeEfh0RbqNqYpI8AjgQYHsX7cgjCoVaTeoUpPPD6QwtbDYfwJuCxwMfD/sbC8LyFUl/eZE+HLh6If7rCWT7sbAewMm62Sn1Qbig6H/Vj8cJvwxKaGMsbUjU43bm4XPcZ381+BeGBvdZpH/eoPUFTV8XWn3qlzsXwA+GvzTcWK+ORB+yjyLMUmuTrWk46aOxSmAAi5+lDJ43MaEn4tYfe1j4mnlF6wPkk40ahbnZgWm5dZ5c/i6qqW2sAn//NMnxqTtDj+Ov2/9RWjC72RtT76T2wHvAbQbvUuIy5+8UiMqEB+uHRN8279dIk9cl6CW3bAJ//yGbtym+ktWKoSoq+Zm/JXXOQcw4Y/ICgUNHfuTk8ulFSR/aaJsHQ5kFY2z2Sd8nN6i7c6vNN1N+Fta5CLhIPfxwDsAhVWe28JoTTimNmYPbdmHwzJbAF/jK/rhlwtCIWNrTagawWmhU1xvYDPC7+JTv4V4vb5iwt8SXh1qy22n27By4bUJiojdOWttyLzD73XuT6rz64cdiKIs9gbOmJT0ZQmbekhnwi/Lbl1Lc9XwpXejkJH2bS0DIpoAgF8A9wS+1lZQE35b5Op7L/70bH0oVB8srTQy4cOOEwjLjO2UaujUKBuF5Somf79wEU2RcG1u2Sqo4tkhm63CX/X/217csksn1cozaac8HccB39skpngmUKylZhzqapfOWlD2+nJfhB+TvTZPCnVuS9LXBPRlcPUuvry9w+91Pk2u81WXhSan0EgCt/Hh15LLaO4+fN1NUHoJpdFYN5WCpq8OaBXplfplsemUN+GPxAgFD9uEaH4MeDjwk4JlLVU05ZFR/hx9zm92t+Gm4Zaz2rcN1ysNgzkTvvhUt21VjUoBEHLprJObStFeuqGteaL05WuXITXhl7Zcxpcnzg1yd+Dd44s0OQlSb9E28dmtMh8WisqcCV8pxt8YMqE+FfjNmja6G/Curnb3ksWEv6ZFKn1dUQXamerKfOuY30qxSVWrWay6/r7RZbbmNm5NN5znSvjXA14PqPrUw4AmUV48XxRe+S/AlxcSrC2bU9rdy42jCJ17AJ9LnXibtTPhd4FifX3EGf68y29n3+aw7SYb5CiK3T4iiMXkau1GHf+tORJ+c0iri3YPBE7dwAzaPCmsUvH456wwlVx8yqaqRHRrRebE45jwx18gpUpwjXBhRBOzK19+kztGOi+mEojTDCzeOk0NcywJS60t3a58ebhsI33jYifKnaOdvRJh6RblT0sSfg1Z4qI6OrycQzK+hpzfH364l2U93Tmk2Pjv8AXwy00wviLwWkCH/4vzZg3T2KWzFngzeFkHRUeHHaoiBdbNojknwtf00M5POcuVJ14pqPX/lff+liGlsD7/tetTBawpPzr3uTigy3tPAfYMykiv5wAKAJA/W7maanuag1WlK055VkXbaKOgLz4d+qrGgMKkO3u8w+8Myio70kJWpIEIqosiHXMjfE0KXWi7DaDKR4qAUlUkffIfH/Lhr3uwN/bEy4llryVfUIx5HGmVYotVhN/gqXKIOvhdJ8rnfPKY8FNMNO822wdfoj5FO5+A84bW2huBLRDQ5kBfgfoR6dSV04xiwveMS0FA4WbyKepz/YSUF9zGCBiBbAR0FnBYODPb6OA3u9P4BRP+WvDN5uXm9qD8lLpMpLhxP0bACHSHQBMkceKahc43lciE353Bau+pCT1TdIHCxP5Uu8LWzwgMhMCFQ01jxel3cWFrQ7FN+ANZ1MMYASNgBMZGwIQ/tgU8vhEwAkZgIARM+AMB7WGMgBEwAmMjYMIf2wIe3wgYASMwEAIm/IGA9jBGwAgYgbER+H+a7uFHaPIt0gAAAABJRU5ErkJggg==" width="190" height="103" /></span></div><div class = "S3"><span class = "S2">Second order discretization of first derivative was given in 2.3b) as</span></div><div class = "S4"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="89" height="38" /></span></div><div class = "S4"><span style="vertical-align:-46px"><img 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" width="187.5" height="103" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">epsilon = 0.0001;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">N = 101;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">dx = 1/(N-1);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">x  = (0:dx:1)';</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">e = ones(N,1); </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">a =  1/dx^2 * e;       </span><span class = "S17">% lower diagonal</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">b = -2/dx^2 * e;       </span><span class = "S17">% main diagonal</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">c =  1/dx^2 * e;       </span><span class = "S17">% upper diagonal</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">D2 = spdiags( [a b c], [-1 0 1], N, N);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">m = -1/(2*dx)*e;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">n =  1/(2*dx)*e;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">D1 = spdiags( [m n], [-1 1], N, N);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = epsilon*D2 + D1;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">f = 2 .* e;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A(1,1) = 1;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A(1,2) = 0;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">f(1)   = 0;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A(end,end  ) = 1;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A(end,end-1) = 0;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">f(end)       = 1;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">T = A\f;</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">clf; plot(x,T);</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsFigure" uid="AA1A3A8C" data-testid="output_9" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="figureElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><img class="figureImage" 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" 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##### SOURCE BEGIN #####
%% 2.1) 
% Determine the coefficients $a$ to $d$ of the central difference scheme:
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_j = a u_{j-2} + b u_{j-1} 
% + c u_{j+1} + d u_{j+2} + \epsilon$$             $$\text{(1)}$$
% 
% where $\epsilon$ is the discretization error. What is the order of accuracy 
% of the scheme? Is the scheme diffusive or dispersive? Assume a uniformly spaced 
% grid ( $\Delta x$ is constant).
%% Solution
% Expand $u_{j-2}, u_{j-1}, u_{j+1}, u_{j+2}$ with Taylor series from the point 
% $x_j$
% 
% $$a u_{i-2} = a \left[ u_i - 2\Delta x \left( \frac{\partial u}{\partial 
% x} \right)_i + \frac{4 \Delta x^2}{2!} \left( \frac{\partial^2u}{\partial x^2} 
% \right)_i - \frac{8 \Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial x^3} 
% \right)_i + \frac{16 \Delta x^4}{4!} \left( \frac{\partial^4 u}{\partial x^4} 
% \right)_i - \frac{32 \Delta x^5}{5!} \left( \frac{\partial^5 u}{\partial x^5} 
% \right)_i + O \left( \Delta x^6 \right) \right]\quad \text{(2a)}$$
% 
% $$b u_{i-1} = b \left[ u_i - \Delta x \left( \frac{\partial u}{\partial 
% x} \right)_i + \frac{\Delta x^2}{2!} \left( \frac{\partial^2u}{\partial x^2} 
% \right)_i - \frac{\Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial x^3} \right)_i 
% + \frac{\Delta x^4}{4!} \left( \frac{\partial^4 u}{\partial x^4} \right)_i - 
% \frac{\Delta x^5}{5!} \left( \frac{\partial^5 u}{\partial x^5} \right)_i + O 
% \left( \Delta x^6 \right) \right]\quad \text{(2b)}$$
% 
% $$c u_{i+1} = c \left[ u_i + \Delta x \left( \frac{\partial u}{\partial 
% x} \right)_i + \frac{\Delta x^2}{2!} \left( \frac{\partial^2u}{\partial x^2} 
% \right)_i + \frac{\Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial x^3} \right)_i 
% + \frac{\Delta x^4}{4!} \left( \frac{\partial^4 u}{\partial x^4} \right)_i +\frac{\Delta 
% x^5}{5!} \left( \frac{\partial^5 u}{\partial x^5} \right)_i +O \left( \Delta 
% x^6 \right) \right]\quad \text{(2c)}$$
% 
% $$d u_{i+2} = b \left[ u_i + 2 \Delta x \left( \frac{\partial u}{\partial 
% x} \right)_i + \frac{4 \Delta x^2}{2!} \left( \frac{\partial^2u}{\partial x^2} 
% \right)_i + \frac{8 \Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial x^3} 
% \right)_i + \frac{16 \Delta x^4}{4!} \left( \frac{\partial^4 u}{\partial x^4} 
% \right)_i + \frac{32 \Delta x^5}{5!} \left( \frac{\partial^5 u}{\partial x^5} 
% \right)_i + O \left( \Delta x^6 \right) \right]\quad \text{(2d)}$$
% 
% and substitute into (1)
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_i = \begin{array}{l}(a+b+c+d) 
% u_i \\+ (-2a-b+c+2d) \Delta x \left( \frac{\partial u}{\partial x} \right)_i 
% \\+ (4a+b+c+4d) \frac{\Delta x^2}{2!} \left( \frac{\partial^2 u}{\partial x^2} 
% \right)_i \\+ (-8a-b+c+8d) \frac{\Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial 
% x^3} \right)_i \\+ (16a+b+c+16d) \frac{\Delta x^4}{4!} \left( \frac{\partial^4 
% u}{\partial x^4} \right)_i \\ + (-32a-b+c+32d) \frac{\Delta x^5}{5!} \left( 
% \frac{\partial^5 u}{\partial x^5} \right)_i \\+ \left[ \begin{array}{c} \text{High 
% } \text{order} \\ \text{terms}\end{array} \right]\end{array}\quad \quad \text{(3)}$$
% 
% Next we match the coefficients in front of the derivatives $\frac{\partial^0 
% u}{\partial x^0}, \frac{\partial^1 u}{\partial x^1}, \frac{\partial^2 u}{\partial 
% x^2}, \frac{\partial^3 u}{\partial x^3}$ on the left and right hand side of 
% equation (3) to obtain an algebraic system for the constants $a,b,c,d$. We can 
% write it in matrix-vector form as
% 
% $$\left( \begin{array}{cccc} 1 &  1 &  1 &  1 \\-2 & -1 &  1 &  2 \\ 4 
% &  1 &  1 &  4 \\-8 & -1 &  1 &  8 \end{array} \right)\left( \begin{array}{c}a 
% \\ b \\ c \\ d\end{array} \right)=\left( \begin{array}{c}0 \\ 1/ \Delta x \\ 
% 0 \\ 0\end{array} \right)$$            $$\text{(4)}$$
% 
% Solving the system in MatLab we obtain

syms dx
A = [ 1  1    1  1
     -2 -1    1  2
      4  1    1  4
     -8 -1    1  8 ] ;
f = [ 0  1/dx 0  0 ]';
abcd = A\f
%% 
% Substituting $a, b, c, d$ into (1) we obtain the finite-difference approximation
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_j \approx \frac{u_{i-2}-8u_{i-1}+8u_{i+1}-u_{i+2}}{12 
% \Delta x} $$             $$\text{(5)}$$
% 
% In order to express the leading term of the approximation error, $\epsilon$, 
% we also substitute $a, b, c, d$ into (3) and obtain
% 
% $$\epsilon = \frac{\Delta x^4}{30} \frac{\partial^5 u}{\partial x^5} + 
% \left[ \begin{array}{c} \text{High order terms \end{array} \right]$$            
% $$\text{(6)}$$
% 
% Thus the scheme is fourth-order accurate and the leading order dicretization 
% error has a dispersive nature (scales with an odd derivative of the solution).
% 
% 
%% 2.2) 
% Determine the coefficients $a$ and $b$ of the following central finite difference 
% scheme for a NON-UNIFORM grid ($\Delta x_j = x_{j+1}-x_j \neq$const.):
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_j = a u_{j-1} + b u_{j+1}.$$
% 
% What is the order of accuracy of this scheme? Would the order of accuracy 
% change for a uniform spacing? Can you conclude any recommendations for designing 
% a non-uniform finite-difference grids?
% 
% _Notation: _$x_{j-1} = x_j - \Delta x_{j-1}, \quad x_{j+1} = x_j + \Delta 
% x_j$
%% Solution
% $$u_{j-1} = u_j - \Delta x_{j-1} u'_j + \frac{\Delta x_{j-1}^2}{2} u''_j - 
% \frac{\Delta x_{j-1}^3}{6} u'''_j + \mathcal{O}(\Delta x_{j-1}^4)$$
% 
% $$u_{j+1} = u_j + \Delta x_j  u'_j + \frac{\Delta x_j ^2}{2} u''_j + \frac{\Delta 
% x_j ^3}{6} u'''_j + \mathcal{O}(\Delta x_j ^4)$$
% 
% 
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_i = \begin{array}{l}(a+b) 
% u_i \\+ (-a\Delta x_{j-1}+b\Delta x_{j}) \left( \frac{\partial u}{\partial x} 
% \right)_i \\+ (a\Delta x_{j-1}^2+b\Delta x_{j}^2) \frac{1}{2} \left( \frac{\partial^2 
% u}{\partial x^2} \right)_i \\+ (-a\Delta x_{j-1}^3+b\Delta x_{j}^3) \frac{1}{6} 
% \left( \frac{\partial^3 u}{\partial x^3} \right)_i \\+ \left[ \begin{array}{c} 
% \text{High } \text{order} \\ \text{terms}\end{array} \right]- \epsilon\end{array}$$
% 
% The linear system for $a$ and $b$ then reads 
%%
syms dx_im1
A = [   1      1  
     -dx_im1  dx  ] ;
f = [   0      1  ]';
ab = A\f
%% 
% Substituting these coefficients we obtain a centered finite-difference 
% approximation for non-uniform grids
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_j \approx \frac{-u_{i-1}+u_{i+1}}{\Delta 
% x_{i-1} + \Delta x_i} $$
% 
% Substituting the Taylor expansion of $u_{j-1}$ and $u_{j+1}$ we can express 
% the discretization error
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_j = \left( \frac{\partial 
% u}{\partial x} \right)_j + \underbrace{\frac{-\Delta x_{j-1}^2 + \Delta x_j^2}{\Delta 
% x_{j-1} + \Delta x_{j}} \frac{u''_j}{2} + \frac{\Delta x_{j-1}^3+\Delta x_j^3}{\Delta 
% x_{j-1} + \Delta x_j} \frac{u'''_j}{6}+ \mathcal{O} ( -\Delta x_{j-1}^3 + \Delta 
% x_{j}^3 ) }_{\epsilon}$$
% 
% One can see already that the leading term of the discretization error vanishes 
% if $\Delta x_{j-1} = \Delta x_j$. We would therefore conclude that the grid 
% spacing should not increase nor decrease too rapidly in space, otherwise the 
% discretization scheme becomes too diffusive (due to the even derivative in the 
% leading order error term). To see the order of accuracy more clearly we define 
% a growth factor $\xi = \frac{ \Delta x_j}{\Delta x_{j-1}}$ to obtain
% 
% $$\left[ \frac{\partial u}{\partial x} \right]_j = \left( \frac{\partial 
% u}{\partial x} \right)_j + \frac{\xi^2 -1}{\xi + 1} \frac{\Delta x_{j-1}}{2} 
% u''_j + \frac{\xi^3+1}{\xi + 1} \frac{\Delta x_{j-1}^2}{6} u'''_j+ \mathcal{O} 
% ( \frac{\xi^4-1}{\xi+1} \Delta x_{j-1}^3 ) $$
% 
% The scheme is therefore first order accurate for non-uniform grids and 
% second order accurate for uniform grids.
% 
% 
%% 2.3)
% For the function $u = \sin (\pi x)$ compute the first derivative $u^{\prime}$ 
% at $x = 0.4$ using the schemes below with $\Delta x = 0.1$ :
% 
% # $$\frac{du}{dx} \approx \frac{u_{j+1} - u_{j}}{\Delta x},$$
% # $$\frac{du}{dx} \approx \frac{u_{j+1} - u_{j-1}}{2 \Delta x}$$
% # $$\frac{du}{dx} \approx \frac{u_{j-2} - 8u_{j-1} + 8u_{j+1} - u_{j+2}}{12 
% \Delta x}$$
% 
% and compare the results with the exact solution. For each scheme, plot 
% the dependence of the discretization error on $\Delta x$ in logarithmic scale. 
% Can you determine the order of accuracy of the scheme from the plot?
%% Solution
%%
u    = @(x)    sin(pi*x);
dudx = @(x) pi*cos(pi*x);
x    = 0.4;

minpow = -5;
maxpow = -1;
resol  = 20;
dx = logspace( minpow, maxpow, resol );

dudx1= (            u(x+dx)-  u(x   )          ) ./     dx  ;
dudx2= (            u(x+dx)-  u(x-dx)          ) ./ ( 2*dx) ;
dudx3= (u(x-2*dx)-8*u(x-dx)+8*u(x+dx)-u(x+2*dx)) ./ (12*dx) ;

e1   = abs( dudx1 - dudx(x) ) ;
e2   = abs( dudx2 - dudx(x) ) ;
e3   = abs( dudx3 - dudx(x) ) ;

clf; 
loglog( dx,e1,'.', dx,e2,'.', dx,e3,'.', dx,dx.^1,'k-', dx,dx.^2,'k-', dx,dx.^4,'k-' );

xlabel('$\Delta x$', 'Interpreter','latex'); 
ylabel('$\epsilon$', 'Interpreter','latex');
legend('(a)','(b)','(c)', 'Location','southeast');
annotation('textbox',[.3 .06 .2 .2],'String','$\Delta x^4$', 'Interpreter','latex','FitBoxToText','on','EdgeColor','none');
annotation('textbox',[.3 .38 .2 .2],'String','$\Delta x^2$', 'Interpreter','latex','FitBoxToText','on','EdgeColor','none');
annotation('textbox',[.3 .55 .2 .2],'String','$\Delta x$  ', 'Interpreter','latex','FitBoxToText','on','EdgeColor','none');
%% 
% Note that the slope of error $\epsilon$ with $\Delta x$ reveals the order 
% of accuracy of the scheme.
% 
% 
%% 2.4) Steady heat conduction
% The steady heat conduction in one dimension is governed by:
% 
% $$- \alpha \frac{\partial^2 T(x)}{\partial x^2} = q$$
% 
% where $T$ is temperature, $\alpha$ is thermal diffusivity and $q$ is internal 
% heat generation. With finite differences we can discretize the equation as 
% 
% $$\frac{T_{j-1} - 2 T_j + T_{j+1}}{\Delta x^2} = - \frac{q}{\alpha} \quad 
% \text{for } j=2, \dots , N-1$$
% 
% Let us assume the case $q / \alpha = f = \sin 2 \pi x$ with fixed temperature 
% on boundaries
% 
% $$T_1 = T_N = 0$$
% 
% We write the discrete problem in matrix-vector form
% 
% $$\mathbf{A}\ \vec{T} = \vec{f}$$
% 
% $$- \frac{1}{\Delta x^2}\left( \begin{array}{cccc} -\Delta x^2& 0       
% & 0  & \dots \\1       & -2      & 1 & \dots \\         & \dots &      &          
% \\\dots &  1      & -2  &  1      \\\dots & 0  & 0  & -\Delta x^2\end{array} 
% \right)\left( \begin{array}{c}T_1 \\T_2 \\\dots \\T_{N-1} \\T_N  \end{array} 
% \right)= \left( \begin{array}{c}0 \\\sin 2 \pi x_2 \\\dots \\\sin 2 \pi x_{N-1} 
% \\0\end{array} \right)$$
% 
% and solve it with MatLab. First we need an analytical solution
%%
syms Ta(x)                                                 
F  = sin(2*pi*x);                                         % Source term
x1 = 0;     xN = 1;                                       % Boundaries of the domain
Ta = dsolve( -diff(Ta,2)==F, [Ta(x1)==0,Ta(xN)==0] )      % Analytical solution                      
figure(1); clf; hold on;                                  % Clean the figure window
fplot( Ta, [x1,xN], 'DisplayName', 'analytical' );        % Plot of the analytical solution
Ta = matlabFunction(Ta);                                  % Convert symbolics to function handles
F  = matlabFunction(F);                                   %     otherwise the evaluation takes too long
%% 
% in order to compute the discretization error

N  = [5,10,20,40];                                        % Number of grid points
eps= NaN(size(N));                                        % Numerical error
for k=1:length(N)                                
    dx = (xN-x1) / (N(k)-1);                              % Grid spacing
    x  = (x1:dx:xN)';                                     % Grid points
    e  = ones(N(k),1);                                    % Auxiliary column vector of N ones
    A  = spdiags([e -2*e e]/dx^2,[-1 0 1],N(k),N(k));     % Matrix of discrete second derivative
    f  = F(x);                                            % Vector of right hand sides
    A(1  ,:) = 0; A(1  ,1  ) = 1; f(1  ) = 0;             % homogeneous Dirichlet BC at x1
    A(end,:) = 0; A(end,end) = 1; f(end) = 0;             % homogeneous Dirichlet BC at xN
    T = -A\f;                                             % solution T = A^-1 * f
    plot(x, T,'.','DisplayName',num2str(N(k),'%1.1e'));     % plot discrete solution
    eps(k) = max( abs(T-Ta(x)) ) / max(Ta(x));            % discretization error
end
xlabel('x'); ylabel('T'); legend('show');
figure(2); clf; 
loglog(N,eps,'-*', N,0.01*ones(size(N)),'kREPLACE_WITH_DASH_DASH', N,N.^(-2),'k-');
xlabel('$N$','Interpreter','latex'); ylabel('$\epsilon$','Interpreter','latex');
grid on;
legend({'Discretization error','$\epsilon=1\%$','$N^{-2}$'},'Interpreter','latex')
%% 
% From the second figure it is clear that we need at least 20 grid points 
% to reduce the discretization error below 1%. We can also see from the slope 
% of error decay that the scheme is 2nd order accurate.
% 
% 
% 
% Let us now replace the source term 
%%
syms Ta(x) 
F  = @(x) ones(size(x));                                  % Source term
Ta = dsolve( -diff(Ta,2)==F, [Ta(x1)==0,Ta(xN)==0] )      % Analytical solution 
figure(1); clf; hold on;                                  % Clean the figure window
fplot( Ta, [x1,xN], 'DisplayName', 'analytical' );        % Plot of the analytical solution
Ta = matlabFunction(Ta);                                  % Convert symbolics to function handles
%% 
% such that the analytical solution is a parabola. Then compute the discretization 
% error as before

N  = [3,6,12];                                            % Number of grid points
eps= NaN(size(N));                                        % Numerical error
for k=1:length(N)                                
    dx = (xN-x1) / (N(k)-1);                              % Grid spacing
    x  = (x1:dx:xN)';                                     % Grid points
    e  = ones(N(k),1);                                    % Auxiliary column vector of N ones
    A  = spdiags([e -2*e e]/dx^2,[-1 0 1],N(k),N(k));     % Matrix of discrete second derivative
    f  = F(x);                                            % Vector of right hand sides
    A(1  ,:) = 0; A(1  ,1  ) = 1; f(1  ) = 0;             % homogeneous Dirichlet BC at x1
    A(end,:) = 0; A(end,end) = 1; f(end) = 0;             % homogeneous Dirichlet BC at xN
    T = -A\f;                                             % solution T = A^-1 * f
    plot(x, T,'.','DisplayName',num2str(N(k),'%1.1e'));     % plot discrete solution
    eps(k) = max( abs(T-Ta(x)) ) / max(Ta(x));            % discretization error
end
xlabel('x'); ylabel('T'); legend('show');
figure(2); clf; 
loglog(N,eps,'-*');
xlabel('$N$','Interpreter','latex'); ylabel('$\epsilon$','Interpreter','latex');
%% 
% Note that no matter how many grid points we take, the numerical solution 
% always coincides with the analytical solution. Even with only 1 interior node, 
% the discretization error drops below the double precision. One can show using 
% Taylor expansion that the error of this discretization scheme scales with 3rd 
% and higher derivatives of the solution, which are zero in this case.
% 
% *Important Note: *Interpolating the numerical solution (e.g. for plotting 
% purposes) linearly on a small number of grid points can create additional errors, 
% although the numerical solution is exact in this case. Always interpolate numerical 
% solutions on coarse grids with an interpolant of the same order as the discretization 
% scheme!
%% 2.5) Friedrich's equation
% $$\begin{array}{rl}\epsilon \frac{d^2 f}{d x^2} + \frac{d f}{d x} &= a \quad 
% \text{ on } \Omega = [0, 1] \\f &= 0 \quad \text{ at } x=0 \\f &= 1  \quad \text{ 
% at } x=1\end{array}$$
%% a) Assume that $f$ is a passive scalar. Explain the physical meaning of each term.
% Friedrich's equation is equivalent to a classical convection-diffusion problem
% 
% $$- f' = \epsilon f'' - a $$
% 
% * diffusion: $\epsilon \frac{d^2 f}{d x^2}$
% * convection: -$\frac{d f}{d x}$
% * generation: -$a$
%% b) Discretize the equation using finite differences on a uniform grid
% Common choice for finite differences are second-order centered schemes. Matrix 
% representation of the discrete second derivative was given in the exercise 2.4) 
% as
% 
% $$f''_i \approx \frac{f_{i-1} - 2f_i + f_{i+1}}{\Delta x^2}$$
% 
% $$\mathbf{D}_2 = \frac{1}{\Delta x^2}\left( \begin{array}{cccc} -2       
% & 1       & 0  & \dots \\1       & -2      & 1 & \dots \\         & \dots &      
% &          \\\dots &  1      & -2  &  1      \\\dots & 0  & 1  & -2\end{array} 
% \right)$$
% 
% Second order discretization of first derivative was given in 2.3b) as
% 
% $$f'_i \approx \frac{f_{i+1} - f_{i-1}}{2 \Delta x}$$
% 
% $$\mathbf{D}_1 = \frac{1}{2 \Delta x} \left( \begin{array}{c c c c}0 & 
% 1 & 0 & \dots \\-1& 0 & 1 & \dots \\   & \dots & & \\\dots & -1 & 0 & 1 \\\dots 
% & 0  & -1& 0 \\ \end{array} \right)$$
%%
epsilon = 0.0001;

N = 101;
dx = 1/(N-1);
x  = (0:dx:1)';

e = ones(N,1); 
a =  1/dx^2 * e;       % lower diagonal
b = -2/dx^2 * e;       % main diagonal
c =  1/dx^2 * e;       % upper diagonal
D2 = spdiags( [a b c], [-1 0 1], N, N);

m = -1/(2*dx)*e;
n =  1/(2*dx)*e;
D1 = spdiags( [m n], [-1 1], N, N);

A = epsilon*D2 + D1;
f = 2 .* e;

A(1,1) = 1;
A(1,2) = 0;
f(1)   = 0;

A(end,end  ) = 1;
A(end,end-1) = 0;
f(end)       = 1;

T = A\f;
clf; plot(x,T);
##### SOURCE END #####
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