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</style></head><body><div class = "content"><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">Exercise 2: Finite Difference Method</span></h1><div class = "S3"><span class = "S2">Date of exercise: 15th May 2019</span></div><div class = "S3"><span class = "S2">Last update: 20th May 2019 by Lukas Babor (Lukas.Babor@tuwien.ac.at)</span></div><div class = "S3"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment active'><h1 class = "S1"><span class = "S2">2.1 Derivation of finite difference scheme from Taylor expansion</span></h1><div class = "S3"><span class = "S2">Consider a continuous function </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="33" height="19" /></span><span class = "S2"> and a grid of </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">N</span><span class = "S2"> discrete points </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="14.5" height="20" /></span><span class = "S2"> with uniform spacing </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="20.5" height="19" /></span><span class = "S2">, such that</span></div><div class = "S4"><span style="vertical-align:-7px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfcAAAAqCAYAAACuohJiAAAR60lEQVR4Xu2dBdTlthGFb8ppyszMzJRCysxtyszMzCmmzJQyc8opM2PKzMyYMp0vq+nR77Ut2dZ7z/KbOSdnN/tsWbqCkWbujPaQiyPgCDgCjoAj4AgsCoE9FtUab4wj4Ag4Ao6AI+AIyJW7DwJHwBFwBBwBR2BhCLhyX1iHenMcAUfAEXAEHAFX7j4GHAFHwBFwBByBhSHgyn1hHerNcQQcAUfAEXAEXLn7GHAEHAFHwBFwBBaGgCv3hXXoiptzFEnPlvQ0SZ/s+NYVJT1H0h8lXVzSL1Zcp9LFH0nSgyTdS9LhJV1a0nsSH2EevVrSEyV9okCFjl8hblObfSJJ95R0GUmnkHQ4ST+X9E1J75b0LEl/nvqRyt9nbL4sYPRwSY+rvD1U/3ySDpB0NkkflXThBbSp2QTGdVtfPT6sM6kms7bs2/HQvyQdVdLfmr+7ck/B6r8bAntJeoekx0p6Swcsh5H0S0nHDr9fWdJbK4JwH0nPlXTaqM45yp3HjxlwYWPw/oltfoGkp0o6eGI5tbx+JkkfCuPmx2Gj9GtJZ5Z03aDozyjp67U0aEX1vIukJ4eyPyvpPCv6zjqK5aDwCEl3ksS6gSxVuV9P0t6hjdeQdMLw979LYux/NwH4/SSdODxzO0m/k/Sq8P/Mk4e2ve/KfR3DuP5vcIpCoR8UlE5XixhPP5R0EklfknQBSX+poPnHkMQu+haSfivp95JOFeqdq9x5/ASSPhB22V8c2W7K+EE4zdxxZBm1vfauYCH5jaTTBPytDQ8ISsCVu3SrsPn8j6SbSXpJbR0d6nuFYIk5maRPSzrvwpV73E0/jZQ7//7anlN5s3vBi7XhDZKumep7V+4phPx3EHiMpHNKumwGHCgnTGycxHYzFWW8v+5HjibpG0ExsxvmdPTMaPIMUe7UnYXr6ZLOKumQEY3hNINC+4MkTNU1bI5GNPP/rxwhtPGwHYsWG68zBCtGDeNpChY57140WMdqtWLcW9L+we10Z0lfDQcB2r7Uk7v1K+42XE3/lXbkmOFU/7GMzr+qpDeG9eFRqedduacQ8t9RUuyuz7FQsyibkU9Jwtz1ttDdr5ug3CkCCwe+YjYKQ+TIkn4k6VjhpRtLeumQAip89ngRv+D5km5ZYRu8yvkIwJ1gQ4cfGvPyWbZIuV8urA24/q4dXHkgB3/pgkHp9yGJ+f0hki4fXKS9qLtyzx+U2/okJlOITPiKligsNPwXk7WmKneIhJDwOHF+awBot5f0jOj5D0vipLZkYXP1s9BAV+5L7uldbYOPg/vFZJuU+/0lPTIodnzoxp8Ai+tLemWi+98sCR4TG+JfpYZKm3KH3PAnSZwiTK4j6TU9hcEEvJukq/eQrVJ1mevvteCBKfnWko7T8FlOwRXz+heCqZnTaJfgB8IfFAsnMBbrGmWqcqfN35HExgiLQI5glsbU+mVJV4teYIOA26BNahmbbXWPMe7CB7cGxKumwOmAj2DMesieEIs+E8h4uFfwSzeFd4j0iIV+ws/Pd+4gCfITfAsYyAjY0webEnzrECxjgXR40k1VqPB3t0m541+/lqRTB24SvCQbW6yh/L3P9YRVD8nq+zblDuuXMIujS7phKIxFh074d0vH3lXSk7SL7PG8wh1PHfDzYjb9fuGyc4ubEx59dSZE7TbB1AMhrISws2RxOa6kf3QUSLgYIWCMJcJYzh6eg8kLo7dGKaHcwQSCXh92MTYodCb/KSW9PDqx94XL1DI228YA2MDj4BDBGEPwv8aRBrCJ79F4GevGEyQRFva14EqBn8DCyOGC8j4XNki2GFoRXcr9QsHMSX2asmnljp8V3gfWJdZYhAgUTnBLkG1S7mwksVwwb/G7m5ne+pGT/aM7OpV1hEikNzU2/51jIGWW/3hgPFPATSW9uFESYSqvCFT8/QqPNOrGTvxcIWb6dDOI/d0kHil4V6Hcvx1OoDlEOurHwLuKJGIvOQmxONcoJZQ7bozXh80pJ/iUQEAk0oAN9Q1CPDPvYH7jpNq1ubJy5zw2+9o+xCwfh4JxoMBvG5/QORG9L1iRUOysHZzo24QDy+nD+MZaAnnxvsH/uWf4OxuLTSt3qzsbDzYtCKRLQi6XINui3DmowjH4YMj/YX0HzwcSLoLFHCsSSrwpWKneKenB4fCd7PuUcr9USCBBQd8Lk+GfodRLBHLACyXdNvml4Q+wU/1rFAOJ7xEf5CZlk3ik2l1auWP6QdnAyoS9nSNmnmexhIhXq5RQ7iRiYc5gBWNC9gmhQFinzh0WcE6lhMyww0cg31CnPpnz2Oyrd65yJxQOFxGWIgie5+8gIJGrwE7/fSFDptyxRvJ3kqnEkQmsjVgLWYM2aZY37GLzPKZdNo5LkG1R7hcLYbJsSu8edRwbTMzzjGuEBGBt+vQ+IWrpShHxt7f/U8qdl9lpGKkHkxhsR5jT/DuTiHi7NnN9iYH3QEk0ipMPfn9OhAgZjcwnNvQ7ZEwbymKOv7FJPPraWlq5w8h8+wB3C4qIGHGELFo3GtoxM3q+hHLHh47lAhJMioyIj5gwGYh4JrhEbJyyY8eEl5K5js2+eucqdw4RWA+RVBQBiyVKA9Mnf2Lub4opd/69S1mSp4GNFrkLNi1PkUToGMLpDhPvFMEaZ+6QMeVA/Cxx2NoW5Q4nDVcd6yLrYyz8O78j6FJcm19pPGNZ6kiAQzhdUnKUO4qdRQPhNMEJ4b0hqw6+IHa26xZMbZYFbei3jUAz9D17fo54ULfSyt38k1lhF0ExYRJFMJfiF61VSih32g7xCbN6my/XsDl5WKjxucfZ/MjOhgUEQUnhi8cy0idzHZt9dc5R7qxTzHkLEYS82fSnx98gux+Zz5AuP6Ypd7Al18HcU9vaxo20zsT+U+8p0sY/GFJem5Ia8r49uy3KnYRDYEZ7m4qb/iSqBjI0QiZQ1t1YCK3F1Yn7KEtylDsFkdsZpY6gzDFXQZ6yk1rWxxb00BzxKK3cLTNYrjvEdqZ08yWD77PWLi+l3PHXYm6zbHdteLBrx+dGGsomw5ukHpC9EDgtxLimZI5js6/OOcod/OykCpsYn3ifoNhR8EiXad6UO6cgSweawnaTv0OSxW+7tPDIbVHuWJPghGBxbrN0Y4rHKm6CZcW4OrwDaRT/fDaRMle5Y56CsGPCqaLN1GW/w6B/WDAlxu9tcnKU/PZQPPg2HALcDJB2CG0Zw1PgRIxLpE3wQWKug3HdRb4iR3HfiScul3hMTj2Uiz84JZAtMZciWFWmbPxI3DLW7YISaDKsU3Vv/l5KuZOClphUFFibsFjTH1xSg6+tKTeR9KLwj1gB8OOnXGBjxuZQfEo+n6PcGYN2IQ9kI1wYfcI4NPJvlzKMCXXMmzkLVhvLP04on5nn51zn3Lptg3LHtQNZjugh5meb4MaDMEn4MYLVjrWe+X6RkPEzd4N/aAG5yp0FCrMAixGCkmLx7xIy7kAO4tSRoxhyB8JcnhuKB2QdFDomFXzTXaSJVPsw23Lr2liB5Gam3lQZdnJnYH0k9XAgOzEwUVbNmPeM13c8gvl5rNvl82EyDP1m/Hwp5c6cIS9/18mdzRqbPciLbe4twrpwhdm8o+/hQfTJ0LE5BacS7+Yod+aP3UK4jcqdED8sEAghhM249xL9sKkytkG52/jlZA5vrUvg3Jhrk2cIbSabHZs5OBeERcLhyZIc5Y6dH+IcvkF8ArwDpZ/dJKaCNiF0h4WJxW1pMhQPlCPmFBjT+MtI7DJWufdhWdosbz45iFwQuvrEMrxhguaCGcLhapZSyh3FjNmXkKymgBVWBk7mfWx6Tmp2gQx5pVnou2To2JxDH+Uo9/jkWtosP5WDsw4MsYLaGLGIinV8dx3f2Ablbib3nFwwbOJsjkP+5oZK1gCseBwCsOBlSUq5c+rgtIgpASVFbCVhOcgmYy1RZG2Zq3IaDWBjzbZj8CCEB9Y0ZjXYvrB+a1DunBLp+5xMc3EMbk7oV04/bfKZEsqdsUK/M1ltzsRtIhMaih0rR9+d95YlkHcx0bFxbmPLjhmbm8TYvp2j3FmnOLEb4WgIoQ5XFBcfNaUms7zljyAMGXdVifwRxE2bG23MOOAUCidkqmyDcme9J3toTmIvrHy4vI8YgCWpDWsx8yTljtrRFynljt+KEDSc+7A1iffErIt/AB8CO+o4TzB+MfxjCIx6I+FNHQDN9zfFlh+KR7PeNSl3u14Q9wtumD6JY3AJjTQTYul+X1d5JZQ75BmSAHHqat63zLwjVpu4bcysKYnnVZeymjo2U3VY1e85yp1vY/G6eagEp5i+606HhMLVcHK3/BG0y3yyU/vD2fJTEcx/H9c0/nMOpKlkVJSKQsddh2CpYuPOXRVNBn1vDfqUOx/ger59GwkT4nhTcsrzjAn+ZIL1DwwxfWNPyFaepZ/F35YKA8qHetyTY/CoWblTdzBnF5kaVHEMLjtPkrfULCWUO9kbuQiCpCoWSmqYWEKLXA4ESs3y9LNhIFtjHApVYmxuqr9ylTvJPiAo4gLKTWJDohdi2NuklpN7nD+CDQ0bmyXJKk7u6DXmGIdQfNhdYYM8x/zkT1zPfc/hD+f3OD1yTj+gmDkIEznTRYZuloN1Bpd2TMTNOWTtKKdLuduujj/jW6p4GcYuFbV7mDmhxGZCSxGZ2l2ngInTz+LbZ3L3mS9T5U35fQoe8XdrOrlTb+4lJx0qeY0tM2EbjhaDSz8Rs1m7lFDuzBtM7xDcLPmS4QIphvmTk5iGd9jx47+3CAKyQ9oiU2psbqrPcpU79eNiF8YkQqYvogzi6IGx6WfnzJaPSVZkNqPdS5JVKPc4rKxNhxl+sfWi77k4tJKy2yJbuvqEDTybUg7FZnnK6T/TFfbsYItom3KnEG6Aw0/VlXaUCcZEQ9gZwVBmsYE4ZuYz/LAH57Si45m5pJ+dikfNyh3yDvn9U6Q6i8HFL2r3j8OL4JRZgxCXH1sniCXldIwQWkgaXhOITXGa0rb2Ma8gvjCPLPOUPccmlVMjIVp94aTNcomFt9uguM+B/PMlx+a6+wl/LyZmiLd2cx5m5zgPP+6g5i1ZMIjJ3mcXx8ALsYtjyATYd3EM5CTeR3AlkRSHsWtWETYKZMSck8T5IyBU4kaAv8MtkLXK/uFUTf2JirHMgz+RRLZGE6J0aPNQIZrAsu/1WTsssQzl5z5H2SlXGgRarnBF2DjCcqctFvHBGolLrk9YQzDn46dHOFQPsl43lTukOZJgsHj07TJI+sDCHV8La0xAlAGTNte/0NfArvSzQzt77PMl8Ii/XdvJnbrDnSBmvY0UZoOuzQw/iNk5toMKvcc4gwiYI1gxui4jsffJ/4xrCkVu8cn2G0SkMTkO4rpBqEKRwW2YMldz2ruqZ3KufMUk3XbDIaRCDhdwgeD9sA7RJ8QRk6YTd0jbla9x/v22dqHcMaPOSSBdNk3xtd97jyULk3lKsH5ZpEjq2fh30rcy/7gSmXliF+40y0AJM4cwt7NRTj3HmILJnlLMcXRDW71zD757h00BvDYjk2bjkCLUZRcUHqTDSONIKr1SxI+hdZjz86tU7qtqN34iEhHxZ9e94qv6dq3lciqHBIfZ2MURcAQcgbUjUFq5k0KTvLncR213wa+9UTP+YI3KHTg51XJzWa6PeMZdsPKqQaSD4EYWx5T5fuWV8Q84Ao7AdiJQWrkbQxgGPUx6l50I1KrcMVXi+8Ifajm7vW93R4DwQbgn+NhyMwE6jo6AI+AIFEegtHK3+Lw46X3xSldcYK3KHcjxax4U0iDWHse+iiEEOQtCKfGpzdC3VXzPy3QEHAFHoBOB0sqdvNewjkl2A1v4EMf+UAS4UhJyBwxKSCKERRDWgpCSto38M0fo9gphIERL2EUec6znuuvEPIIghrXKcVk3+v49R8AR2A2B0sqdUAa7b/aAkHLPYd+VB6ArdSDhObWEjHlfOgKOgCPgCFSAQGnlXkGTvYqOgCPgCDgCjsCyEXDlvuz+9dY5Ao6AI+AIbCECrty3sNO9yY6AI+AIOALLRsCV+7L711vnCDgCjoAjsIUIuHLfwk73JjsCjoAj4AgsGwFX7svuX2+dI+AIOAKOwBYi4Mp9Czvdm+wIOAKOgCOwbAT+Bx5uEmciZKDTAAAAAElFTkSuQmCC" width="251.5" height="21" /></span><span class = "S2"> </span></div><div class = "S3"><span class = "S2">where </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="17" height="20" /></span><span class = "S2"> and </span><span style="vertical-align:-7px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAoCAYAAACM/rhtAAADJklEQVRYR+3XWchucxQG8N8xhMwnknBj7nSclCFEhgwh4wXlHOM5XLg1pEwZMiTCBReGMkYpRKZIphQZypghRSKZIhky9Wh9tc/+9v6+zft+p6+86+bd7f9a//XsNTxrvQvMc1kwz/GZABw1Q5MITiI4agRGtZ/U4P8ygnvg5caX/4rt8FlPNNbGU6WzFz4ZNWpN+64a3B0nYRH2L+VbcEaH49XwAA7EvnhjnOBy10xNsklFYz38jh3xcQvATViOw/H0uMHNBjDnl+P8cnwPljVAXIBL6929cwFuCMCNK4ob4k8swTs4DbfhbFw7V+CGAIzORbikQDxYwB7CjThrLsENBbhBRXFhgfkZAbgUf80HgMFwHq4sMJ9ja/zWA+4+HN84S5Sv69DdFh+23v+C9asp/zkaOuoOxpONy/bGSz0AU69r4m1shm+xDb5v6a+BjXBCUdh++APfzcaDbb/hwxcrYnEYeRYHzJDeTfEVfsK6uAbn9ujfUEBP7jqfLYJb1FT5Bonia9iqLgo5P9Pj9CDcX811PTKNtsenHfrPIc0XvWkyE8Ck6gWEqDPCvsQKZKpEMg7zvkvOwaE4pFIdcHfjxJZy/CelR+L5fwNwLTyBxQViqphTN+8hBR7JBHms4+IQ9xdFQ3H+cHX8Lq1xmGb7qFL8w1CAma/pxMOqzl5pGaaoM1UiryNO2/Iurqio5SylkJrNb0pjSo7F1bVodKaiK8Up2jMr7I93WOUD3sROdXYHvsateB/r4EfsXOmNWp5Tv7HNh0/dexl2wHE9pTKNZtJp+aJTEMd9clSRdfM8K1nSlW0ohb8Sn+F2nIq3CnBG5yNFV1cNBTgDpsFHWctOx24ti82LmEM72YACODtmGq/JsSuZzUYzg1E1FG/G6j3744W1AWUa7Vm0E24NZw6uwf8CqmkT+rkL2RXbkvr8AFtWw2THzHOvjDuCaYLQRYi6+behCSBceGe9eBRHrAqASWmaIjP31Zo26eQubktQQl27VrovXhUAj65x1fSVbs2C2yX71OQ4poMN5rxJRq3hCcBJBMcagVEvGzcPjopnmv28B/g3Ne2OKVUIrdMAAAAASUVORK5CYII=" width="20" height="20" /></span><span class = "S2"> are the boundaries of a domain </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="81" height="21" /></span><span class = "S2">. "Discretization" of the function </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="33" height="19" /></span><span class = "S2"> on the grid defines a column vector </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="13" height="27" /></span><span class = "S2"> containig the values of the function </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="33" height="19" /></span><span class = "S2"> evaluated at the points </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="14.5" height="20" /></span><span class = "S2">, i.e.:</span></div><div class = "S4"><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="99.5" height="29" /></span></div><div class = "S3"><span class = "S2">With finite difference method we approximate the derivative of the function </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="33" height="19" /></span><span class = "S2"> at some point </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="14.5" height="20" /></span><span class = "S2"> using the values of the function evaluated at grid points in the neighbourhood of the point </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="14.5" height="20" /></span><span class = "S2">. For example, the second-order centered finite-difference approximation to a first derivative is </span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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R/v/+S5ntDzz2yMAAAAASUVORK5CYII=" alt="SecondOrderCenteredDifference.PNG"></div><div class = "S3"><span class = "S2">Finite-difference schemes can be derived from Taylor expansion of the function </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">u</span><span class = "S2"> around the point </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="14.5" height="20" /></span><span class = "S2">. This also provides the expresion for the error term </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJwAAAAqCAYAAABGKzIlAAAJ4UlEQVR4Xu2befRu1RjHP5lZLPM8zyFDLOOSmYRIppSMy7BkzhAh8ywqFipDFGXOUJGhzEsKS2UqCpnJUOawPjy79j33nLP3ed/7Hvfn7uefu3737Ok85/tM32e/m9GkaWBGDWw2415tq6YBGuAaCGbVQAPcrOpumzXANQzMqoEGuFnV3TZrgGsYmFUDDXCzqrtt1gDXMKAGrgqckqniUcBpwAuAGwO/A/YGXrGsuhrgztHgZYH7A3cMJV8KuCDwa+DHwJHA+4BvLaD0awN7Ag8Bfl853/P8onLsssN817sDjwDuFOC6IfBh4BLAs4ALADcFvh6bXQV4HbAL8PPaAzTAgR/2xcBDgfMHwL4cSjw3cCVgqwDfP4G3ArsCf6xU8vWA9wD3A06unOOwt8WH/8aEOcsO/SxwB+DA0Me/YsG9gCcBO8eztM+WwH7AtsDPajbf1AG3PfAWQAs/Btgd+DQgsHK5EPAcYDdAEH4xPMIZBSVfATgK2CnWr/kmjrkccGp8zCfUTtoA434LXBi4IvCrbL2Xx7vfC/h4Z587A68OoP6hdIZNGXBPBLRcdbAP8FTgrILCngm8Msbogcx1hsR1BebHgJeVPkTn+UsC/IZfQfunifMXGX414IdhcHfpLHAw8CBAb/2dnsVfBTj/gaWNN1XACTaTYGV/4NElRcXzc8VHMX8x3JjTDIW8x0Xusznw18r1HaY3NWc0d1IM9e+aMH/RodsBHwKeHylGvs63o7C4yIBR+v+mC4+NNUatcNEDrtV5twC+AJw3rNUq7G8TXua1wNNivJZtQt0Vw9KPospLwK7d4vHAG7PBnwduVzt5iXFWpHsA9wY+mq2jAZivfg245cj6LwzjuNZYpJjq4bS6awBXDwvXEo8F/rHEi8459TzAiYBVo9JVbs1ZDKN6ReU44GY9k/SgrwEuM6EqdRnzQ0PW8YAeJ4le8rsDh9PrCgiBkcTw996RlzHnMoW4bwYuK9L7AHpvv2uSWwEWUfuGBxta1nnmnTsAhwwNqgWcoeMZEaNVyC+B2wDnC77G0vjQmq/1Px7zMOAdcYbvAddd4DzmKUmhclVWsV0xzEoVSDVMEUEm9aJBH5R5NsGr/vvk4hECLxq0i2P8RlsMeJqnBJ1hGpEMxznycHpmC6hcTA3eBOh5/XdMNECxMfjeJcD5XEswjJwZ1VYClnzVZ2J3cxRfeEquMuVDbKixcmh+CMWq0+prqsilpZzKpP5inQWuHOF0kfU/F3Pdw8pWekKxYhTYpdCvJ9IjKQ8HDuicTe/z7gj1L8qe+Q6nDxQMbw7PtnUUQeJgSEwfHhOg7a3gS4CTe7GSUyRFP5Dt5FxJUcOs5bSKnqOamgqQNN7c4vvZ5BstSOKasyXG/aQsPKel5areCdwtyOLa894c+GqEaD2FROtPAT2Y8gDg/YXFrC4lqBUrTj343+NvCd3DgbcDeq1c5N7k4HQsT+88+0qWu2loFjFDIshdX6okOaN1xo4BzpxAN3vp+DAm14kITIs8OYAocfrJWs3GOC1GZntRMbE2oa4Vw/4bYrCGYn7VfZ+atSR+HxkDPwXctTNJ2kT6xDxRQNaK1IMktJEjyesBdax8ojJEH52F4hQGbwL4/4JKArpE/9SeuTvu9sE7eubeYmkMcCrMPEeRTdZVbkiR0JT/WlS6rHdpHS1PC1Q0DgG/iNja8QMqgksyOBe9kB/VtthfKjewlymtYA4nb5fkBlFA+LfGYW5nYj4mVrSCS9FD6vUks38QxvHnyjMtMixFEQ3FVGw9GQOccV237L/mFrrdRTzCIgdfxRxdfPIeAt10YapcMvKppDctWt3kYkhzHyviWrHPeg/g+j1dDsljCzTFvEvqoiSeIZG3AsxIddtIfUpzl3l++QC5xp2iwDrrlXK4baJ36EJ6BfkrKxkVr8VMZdCXeZll50o16DEU8zA5tKmSFww21k3ku5SQALHHmNMUY/tYbElDWIXaZutKXln/JBj9UkhMVEZay/eWDlq1mM//Jqp4C5T1ZAxwPjPs2KjWWuyTSQNYHPjMGG0ltlbkS8Ct47C6e93+VMm95BBop3o4k3TDsnrtC3cC19AoMJV7AocVDm5+ajqU5jwXeOnUl11gvG04MTLZw8mvWZJbGdnINt+S+NOyBJtkY8nKFjjvSqek3MpN+to3pc0leG3w+/5yTeYrfTdG0j5WmSWayG6HuZvcoGcaElOA1MSXoJWwHRIjkMWBeaGcmueV8jD/q70aVdLF0PPrBEHttaXUjVln7JCHE1ypv7jIx6k5sLTBWIldWkMS0vBVK3mHQC5KnqtW1JO3PkzIzWPNt44YmCyLr9cSkKXrSA8OsMnSj919k8L5ZuynoRvK++6gmTdadBhSvVL1vHAaTvVCgH+vUqReLFA0jrw9d/aefYC7ZvBVPjM/sVSXZ9vQMneVan5h8myj2Rusuv/ais0+YfJAhiZD1JBoRBKu0iXSJkOifvWYAmns1kman/Nhzx64feu+trVMhaxUbYmZu9oy0xvr5cyxViXJqC2aNND1pA9wejY9nGIDWtc8JHJzJqR6jLUgORc31i7K38U8Ve+grkpgc569Zj2beVm6ytSnm8RZebNWUJTEqk8OUJHfM3zlrIFdE/k/W285QZ/TQXpfx6xK7EpocBaVvcbcB7i8V6j79g5UztCnw3pJzxeTczJRXAti7qkXsNpULHz0XH25jWFJoMma6x0sNNIHL72rANJYDb1D8pHoRdf2W83NLB700Irhy1xNSdGiL5R5T83Gv3m5nSAjWPWV8NKLdp6fEMbmpYhe6QOchKXNZy1IsTqV/tClCyxDkx/BLoFc1lAuM/Gssw33nQWZVabvan/SjoUAMck3hfAKkwZlSuGtC28C5z8yKR3Wyl5vaLXYdwvWlpMNdvedQlcIYKtZJeWhGrxntN3mOfvEDoveXbHSlrwWrN3bu6X3GnueCgbJ68GLHENFg0o3wbS7YCWVi705F/SjeTFvrYqJt90K8x2t3hae72ajXEv1g3hzI7+qU/uueiHnCYC+5NmCp9vPrF07jdM4vCL/wQBfL9Eag+VRDcM5N9i9LTJ1/+54UxSvN2lM3Sv6Z48tEb92GWxxmWwqunQtchVFxLIvvLHN16MYhu0elG55bGxnn3oeo56NACv/Ua9ZAtzUjdv4czSgbq0UJWmX/j3nRq5YiwVvtVghj0oDXElDyz03lEkPWKRIgfw/ij8R9Hq6vfbiTycb4FYPAZNpk3qr/3T7ZvW7zrOD3Rf7v/58sKrybYCb58PYdfAi644ztJfmeaP//vZBWsnipwpsHqwBbq7P0/b5jwYa4BoQZtVAA9ys6m6bNcA1DMyqgQa4WdXdNmuAaxiYVQP/BhFm3jr6BICzAAAAAElFTkSuQmCC" width="78" height="21" /></span><span class = "S2"> where </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">n</span><span class = "S2"> is the order of accuracy of the scheme. The derivation of a finite-difference scheme procedes as follows:</span></div><div class = "S3"><span class = "S2">We start by assuming a certain form of the scheme, where we select which points we want to use. Taking the example above we have</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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" width="178" height="44" /></span><span class = "S2">                 </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">Next we expand the values of the function </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="63.5" height="21" /></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="14.5" height="20" /></span><span class = "S2">:</span></div><div class = "S4"><span style="vertical-align:-22px"><img src="data:image/png;base64,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" 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" width="430" height="54" /></span><span class = "S2">             </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAkCAYAAAAw55zoAAAFg0lEQVRoQ+2ZdYhtVRSHv2cnBnbiU1FRERMDW7ETu1uxxQBRTBQ7wHgGKNiKiomKnRioiCL+Y2Bji2IHn6wN55579j7nvpmRGbgLHo+Zvc/ae/32it9aM4mh9CAwaYhHLwJDQGoeMQRkhICsCSwF3DxBQu1U4Drgy6737eoh0wMXA0cBHnJOwwHu2QDYBFgDWBaYG/gb+AZ4G3gAuBH4ueH7g+Ly1SUNWaCrMQ37XgWWAQ4E7uqipwsgMwAPhaGCciLwT035usB9wFzx+/eAp4FPgHmBVYF1Yu1zYCfgxZoOvW+3+N3uwHzxsiMBZB7gYWB14CTgwjZQugByC7AHcCewa0ahBqYX8GCB0zOqsk3omAn4AVghAGtS+VqAOFIPUbfAvgEsCOwJ3FYCpQ2QncMIDVga+KoFEF9jq8KBvtAJsX42cFpm72gC4hG7AHcA3wPLAV/k7lgCZDrgA2CRePFkSJOujYAL4p+elJOtI4+4fi+w4/8EyDSAYWxBuB44eGoAMZ6Te60SbtcWgm3res+DsenWcOGxDpmk/8zwyF/jkU30fVLyEN1/C+DriMN6Im0zvmn9XODkWNgHuKmjh5iYjwO2AxaL/PQuYH6bAvzR4TIm9edj3+HA1YMAMiPwLTAL8CSwcYcD27asDDwLzAY8AWwG/NUBkA2Bx4A5AXOLxqvLCqK8Hrp8uJLMHslcJ7Aibj8IIJbAl+IDkRTRQWRaYAlgVmAysDmwL+Blrgov0XVzkpKqbv1pAHF0hb+Y384ATgkFrwBrFwBO53wc4SJ4el2f5ELGy0uglNOBswZBIw718KrIS+QwGtsmCRD3PQes38B9XDOBWwmVY4HLWxRX9Uoav6vvzwGSEpD7s/FWOHzmKL+yV3nAesC2gJ5jbvK13y98X724eeP+zF4JXwLYirhkBrj0ecqL/ixZ63ucHCCXBuJ+uH/FW9petrS+YjDeRSNRmxuk801SBcTcIQ/KibkuMWTbBctrTu4BdohF86L5sUdygFxbqdWyO0vkaIhx/kIoEoyVGhitywmQH4E5Wg5+OXont0kVJGA5kUak9qDR87oAsleUt9EARB02XKuFMiuNFaQugzBVv980FBwJXFm46O2V9sMQttns5CGXRN138wHADaOFBnAFcEToy9H3sQKkGjKy66e6AmKPYWJVvLylcrSkmrBzJX2sQuaR4Cza0si+cyFj3khDIA2w5pfkGeBN4JgOqFW977wKc61+2jWpen+TqolXaUuqkjhJnWJuMkd1CplqOXPidEiLoZIsa/pCLWVPNc5B1gp9zj2M67pUAWmM9fjAXGROUrqUXWcxzlf837v2Sc5DZIKyOVGUGMkjSiIg0n3nJaVuVz16k+LLymb7XqlSZdwnobNEN0mVmNnrXFa4pKXZMxUrUao2PZ+Umru7oz13hmDfkOs7VJgA0TiZY1PlsOSa1OYPL9q7UL2Sh6jXptLw1eA0emyi7jZvfxYAMYnaQylZblUCpNqqa0zqbZrOtFly1uHcQdGN9SwHSjZVhkh6ZUPL8ljnNs5hHeQolnqBc2LmXgH5vdLcmRBTc+c0zPKdG16l+54fY0QfbWHgpyZDSoC49k5MmK4BDiug75IMVLLjoHn5iFGbO1/Z8HsLeDSA6OshgNKQ2XGjvYqvbA7QE1L7b6Vqa//1qA8DiIuip2o0p22EmNzslwDmoxZQxuvyoTE3+SzsaMpb/929DRD3iOjxwft1zVKcjkdAbPgMYecwWwKPly7ZBRD3yFQdCVgi9wN+G4+WN9xJMAxTp2zeu7Un6wJIOkcv8Q9UdsJpDDjecTHPOPWT79T/DjRVOaT+0eKRMJ0rTASxvNrhlqZzPXYM4iETAYAR33EISA3CISBDQMpR9S829DM0c70+bgAAAABJRU5ErkJggg==" width="34" height="18" /></span></div><div class = "S3"><span class = "S2">and substitute the expansions into the expected form</span></div><div class = "S4"><span style="vertical-align:-25px"><img src="data:image/png;base64,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" width="638" height="60" /></span><span class = "S2">         </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">Now we have to form a system of two algebraic equations to determine the coefficients </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">a</span><span class = "S2"> and </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">b</span><span class = "S2">. This can be done by matching the derivatives on the left and right hand side of equation (4):</span></div><div class = "S4"><span style="vertical-align:-44px"><img src="data:image/png;base64,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" width="173" height="97" /></span><span class = "S2">                 </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">which leads to </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="137.5" height="37" /></span><span class = "S2"> . Substituting </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="28.5" height="19" /></span><span class = "S2"> into (2) provides the finite difference scheme (1). We still have to determine the order of accuracy through the error term </span><span style="font-family:Symbol, 'DejaVu Serif', serif; font-style: italic; font-weight: normal">&#949;</span><span class = "S2">. For that we substitute </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">a</span><span class = "S2"> and </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">b</span><span class = "S2"> into (4):</span></div><div class = "S4"><span style="vertical-align:-25px"><img src="data:image/png;base64,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" 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width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">thus</span></div><div class = "S4"><span style="vertical-align:-25px"><img 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" width="253" height="60" /></span><span class = "S2">                </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">which has two important consequences. Firstly, the scheme is second-order accurate since the leading error term is proportional to </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="27" height="20" /></span><span class = "S2">. Secondly, the leading error term does not depend on </span><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="26.5" height="40" /></span><span class = "S2"> , so it does not contribute to artificial diffusivity.</span></div><div class = "S3"><span class = "S2">In the same way one can derive finite-difference schemes for a non-uniform grid spacing </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="87.5" height="21" /></span><span class = "S2"> . Although the schemes for non-uniform grids have often lower order of accuracy, they allow localised refinement of the function which can be a significant advantage. Using sensible non-uniform grids is therefore generally more efficient.</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 Matrix representation of finite difference schemes</span></h1><div class = "S3"><span class = "S2">The finite difference scheme (1) defines a vector of approximate first derivatives of </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="33" height="19" /></span><span class = "S2"> at grid points </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="14.5" height="20" /></span><span class = "S2">. For simplicity we will use the notation</span></div><div class = "S4"><span style="vertical-align:-20px"><img src="data:image/png;base64,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" width="90.5" height="46" /></span></div><div class = "S3"><span class = "S2"> Our aim is to represent the finite difference derivative </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="32" height="25" /></span><span class = "S2"> with a discretization matrix </span><span style="vertical-align:-8px"><img src="data:image/png;base64,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" width="22.5" height="23" /></span><span class = "S2"> such that</span></div><div class = "S4"><span style="vertical-align:-8px"><img src="data:image/png;base64,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" width="85.5" height="30" /></span><span class = "S2">                </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">where the superscript </span><span style="font-family:'DejaVu Serif', serif; font-style: normal; font-weight: normal">1</span><span class = "S2"> denotes the first derivative, while the subscript </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">x</span><span class = "S2"> denotes the direction of the derivative (for the case of partial derivatives). Compilation of the matrix from (1) at interior grid nodes </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="69" height="21" /></span><span class = "S2"> is straightforward. Its only non-zero entries are the first lower and upper diagonal corresponding to the coefficients </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="57.5" height="38" /></span><span class = "S2"> and </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="65" height="37" /></span><span class = "S2"> respectively. The centered scheme is, however, not defined for boundary nodes </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="41" height="21" /></span><span class = "S2"> (the first and the last row of the matrix). We can approximate the derivatives on boundaries by one-sided differences, e.g.:</span></div><div class = "S4"><span style="vertical-align:-36px"><img src="data:image/png;base64,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" width="215.5" height="83" /></span><span class = "S2">             </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span></div><div class = "S3"><span class = "S2">The discretization matrix then reads</span></div><div class = "S4"><span style="vertical-align:-102px"><img src="data:image/png;base64,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" width="282" height="215" /></span></div><div class = "S3"><span class = "S2">In MatLab we can construct such matrices with the command </span><span class = "S5">spdiags</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">N = 4;                                     </span><span class = "S9">% Number of grid points</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">dx = 1/(N-1);                              </span><span class = "S9">% Grid spacing</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">a = -1/(2*dx) ;                            </span><span class = "S9">% Coefficients of FD scheme</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">b =  1/(2*dx);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">e = ones(N,1);                             </span><span class = "S9">% Column vector of ones</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">D_x = spdiags([a*e b*e], [-1 1], N,N );    </span><span class = "S9">% Matrix with D_x(i,i-1)=a; D_x(i,i+1)=b</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">D_x(1,:  ) = 0;                            </span><span class = "S9">% Replaces first row of the matrix</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">D_x(1,1  ) = -1/dx;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">D_x(1,2  ) =  1/dx;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">D_x(N,:  ) = 0;                            </span><span class = "S9">% Replaces last row of the matrix</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">D_x(N,N-1) = -1/dx;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">D_x(N,N  ) =  1/dx;</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">spy(D_x);                                  </span><span class = "S9">% Plots the sparsity pattern of the matrix</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="F440B8EA" data-testid="output_0" style="width: 1171px; 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"></span></div></div></div>
<!-- 
##### SOURCE BEGIN #####
%% Exercise 2: Finite Difference Method
% Date of exercise: 15th May 2019
% 
% Last update: 20th May 2019 by Lukas Babor (Lukas.Babor@tuwien.ac.at)
% 
% 
%% 2.1 Derivation of finite difference scheme from Taylor expansion
% Consider a continuous function $u(x)$ and a grid of $N$ discrete points $x_i$ 
% with uniform spacing $\Delta x$, such that
% 
% $$x_i := x_1 + (i-1) \Delta x \quad \text{for} \quad i=1 \dots N$$ 
% 
% where $x_1$ and $x_N$ are the boundaries of a domain $\Omega = [x_1, x_N]$. 
% "Discretization" of the function $u(x)$ on the grid defines a column vector 
% $\vec{u}$ containig the values of the function $u(x)$ evaluated at the points 
% $x_i$, i.e.:
% 
% $$\vec{u} \equiv u_i := u(x_i)$$
% 
% With finite difference method we approximate the derivative of the function 
% $u(x)$ at some point $x_i$ using the values of the function evaluated at grid 
% points in the neighbourhood of the point $x_i$. For example, the second-order 
% centered finite-difference approximation to a first derivative is 
% 
% $$\left( \frac{\hat{\partial} u}{\partial x} \right)_i = \frac{u_{i+1}-u_{i-1}}{2 
% \Delta x} =\left( \frac{\partial u}{\partial x} \right)_i+ \epsilon$$                 
% $$\text{(1)}$$
% 
% 
% 
% Finite-difference schemes can be derived from Taylor expansion of the function 
% $u$ around the point $x_i$. This also provides the expresion for the error term 
% $\epsilon = O(\Delta x^n)$ where $n$ is the order of accuracy of the scheme. 
% The derivation of a finite-difference scheme procedes as follows:
% 
% We start by assuming a certain form of the scheme, where we select which 
% points we want to use. Taking the example above we have
% 
% $$\left( \frac{\partial u}{\partial x} \right)_i = a u_{i-1} + b u_{i+1} 
% - \epsilon$$                 $$\text{(2)}$$
% 
% Next we expand the values of the function $u_{i-1}, u_{i+1}$ with Taylor 
% series from the point $x_i$:
% 
% $$a u_{i-1} = a \left[ u_i - \Delta x \left( \frac{\partial u}{\partial 
% x} \right)_i + \frac{\Delta x^2}{2!} \left( \frac{\partial^2u}{\partial x^2} 
% \right)_i - \frac{\Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial x^3} \right)_i 
% + O \left( \Delta x^4 \right) \right]$$            $$\text{(3a)}$$
% 
% $$b u_{i-1} = b \left[ u_i + \Delta x \left( \frac{\partial u}{\partial 
% x} \right)_i + \frac{\Delta x^2}{2!} \left( \frac{\partial^2u}{\partial x^2} 
% \right)_i + \frac{\Delta x^3}{3!} \left( \frac{\partial^3 u}{\partial x^3} \right)_i 
% + O \left( \Delta x^4 \right) \right]$$             $$\text{(3b)}$$
% 
% and substitute the expansions into the expected form
% 
% $$\left( \frac{\partial u}{\partial x} \right)_i = (a+b) u_i + (b-a) \Delta 
% x \left( \frac{\partial u}{\partial x} \right)_i + (a+b) \frac{\Delta x^2}{2!} 
% \left( \frac{\partial^2 u}{\partial x^2} \right)_i + (b-a) \frac{\Delta x^3}{3!} 
% \left( \frac{\partial^3 u}{\partial x^3} \right)_i + \left[ \begin{array}{c} 
% \text{High} \\ \text{order} \\ \text{terms}\end{array} \right]- \epsilon$$         
% $$\text{(4)}$$
% 
% Now we have to form a system of two algebraic equations to determine the 
% coefficients $a$ and $b$. This can be done by matching the derivatives on the 
% left and right hand side of equation (4):
% 
% $$\begin{array}{lrl}\left( \frac{\partial^0 u}{\partial x^0} \right)_i 
% : & 0 = & a+b \\\left( \frac{\partial^1 u}{\partial x^1} \right)_i : & 1 = & 
% (b-a) \Delta x \\\end{array}$$                 $$\text{(5)}$$
% 
% which leads to $a=-\frac{1}{2 \Delta x}, \ b=\frac{1}{2 \Delta x}$ . Substituting 
% $a, b$ into (2) provides the finite difference scheme (1). We still have to 
% determine the order of accuracy through the error term $\epsilon$. For that 
% we substitute $a$ and $b$ into (4):
% 
% $$\left( \frac{\partial u}{\partial x} \right)_i = \left( \frac{\partial 
% u}{\partial x} \right)_i + \frac{\Delta x^2}{3!} \left( \frac{\partial^3 u}{\partial 
% x^3} \right)_i + \left[ \begin{array}{c} \text{High} \\ \text{order} \\ \text{terms}\end{array} 
% \right]- \epsilon$$            $$\text{(6)}$$
% 
% thus
% 
% $$\epsilon = \frac{\Delta x^2}{3!} \left( \frac{\partial^3 u}{\partial 
% x^3} \right)_i + \left[ \begin{array}{c} \text{High} \\ \text{order} \\ \text{terms}\end{array} 
% \right]\equiv O(\Delta x^2)$$                $$\text{(7)}$$
% 
% which has two important consequences. Firstly, the scheme is second-order 
% accurate since the leading error term is proportional to $\Delta x^2$. Secondly, 
% the leading error term does not depend on $\frac{\partial^2 u}{\partial x^2}$ 
% , so it does not contribute to artificial diffusivity.
% 
% In the same way one can derive finite-difference schemes for a non-uniform 
% grid spacing $h_i = x_{i+1}-x_i$ . Although the schemes for non-uniform grids 
% have often lower order of accuracy, they allow localised refinement of the function 
% which can be a significant advantage. Using sensible non-uniform grids is therefore 
% generally more efficient.
% 
% 
%% 2.2 Matrix representation of finite difference schemes
% The finite difference scheme (1) defines a vector of approximate first derivatives 
% of $u(x)$ at grid points $x_i$. For simplicity we will use the notation
% 
% $$ \hat{\partial}_x u_i\equiv\left( \frac{\hat{\partial} u}{\partial x} 
% \right)_i $$
% 
%  Our aim is to represent the finite difference derivative $( \hat{\partial}_x 
% )_i$ with a discretization matrix $\mathbf{D}_x^1$ such that
% 
% $$\hat{\partial}_x \vec{u} = \mathbf{D}_x^1 \cdot \vec{u}$$                
% $$\text{(8)}$$
% 
% where the superscript $1$ denotes the first derivative, while the subscript 
% $x$ denotes the direction of the derivative (for the case of partial derivatives). 
% Compilation of the matrix from (1) at interior grid nodes $x_2 \dots x_{N-1}$ 
% is straightforward. Its only non-zero entries are the first lower and upper 
% diagonal corresponding to the coefficients $a=\frac{-1}{2 \Delta x}$ and $\ 
% b=\frac{1}{2 \Delta x}$ respectively. The centered scheme is, however, not defined 
% for boundary nodes $x_1, x_N$ (the first and the last row of the matrix). We 
% can approximate the derivatives on boundaries by one-sided differences, e.g.:
% 
% $$\begin{array}{lr}\text{Forward:} \quad & \hat{\partial}_x u_i = \frac{u_{i+1} 
% - u_i}{\Delta x} \\\text{Backward}: \quad & \hat{\partial}_x u_i = \frac{u_{i} 
% - u_{i-1}}{\Delta x}\end{array}$$             $$\text{(9)}$$
% 
% The discretization matrix then reads
% 
% $$\hat{\partial}_x \equiv \mathbf{D}_x^1 = \left( \begin{array}{ccccc}\frac{-1}{\Delta 
% x} & \frac{1}{\Delta x} & 0 & \dots \\\frac{-1}{2 \Delta x} & 0 & \frac{1}{2 
% \Delta x} & 0 & \dots \\0 & \frac{-1}{2 \Delta x} & 0 & \frac{1}{2 \Delta x} 
% & \dots \\ & & \dots \\\dots & 0 & \frac{-1}{2 \Delta x} & 0 & \frac{1}{2 \Delta 
% x} \\ & \dots & 0 & \frac{-1}{\Delta x} & \frac{1}{\Delta x} \end{array} \right)$$
% 
% In MatLab we can construct such matrices with the command |spdiags|
%%
N = 4;                                     % Number of grid points
dx = 1/(N-1);                              % Grid spacing
a = -1/(2*dx) ;                            % Coefficients of FD scheme
b =  1/(2*dx);
e = ones(N,1);                             % Column vector of ones
D_x = spdiags([a*e b*e], [-1 1], N,N );    % Matrix with D_x(i,i-1)=a; D_x(i,i+1)=b
D_x(1,:  ) = 0;                            % Replaces first row of the matrix
D_x(1,1  ) = -1/dx;
D_x(1,2  ) =  1/dx;
D_x(N,:  ) = 0;                            % Replaces last row of the matrix
D_x(N,N-1) = -1/dx;
D_x(N,N  ) =  1/dx;
spy(D_x);                                  % Plots the sparsity pattern of the matrix
%% 
%
##### SOURCE END #####
--></body></html>

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