Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="734374.fig.0011a" src="https://static.hindawi.com/articles/jam/volume-2013/734374/figures/734374.fig.0011a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>  IETAM</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="734374.fig.0011b" src="https://static.hindawi.com/articles/jam/volume-2013/734374/figures/734374.fig.0011b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>IEBOGEY</td></tr></table></td></tr></table>

<table>Plots of IETAM versus <svg height="12.4375" id="M560" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.6750002 12.4375" width="8.6750002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
l5 26q38 4 74 13.5t57 17t25 7.5q12 0 4 -32l-104 -443h2q35 38 97 93q39 35 65.5 56t62 41.5t58.5 20.5q19 0 30.5 -10t11.5 -22z" id="x1D458"></path></g>
</svg> and EBOGEY versus <svg height="12.4375" id="M561" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.6750002 12.4375" width="8.6750002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
l5 26q38 4 74 13.5t57 17t25 7.5q12 0 4 -32l-104 -443h2q35 38 97 93q39 35 65.5 56t62 41.5t58.5 20.5q19 0 30.5 -10t11.5 -22z" id="x1D458"></path></g>
</svg>.</table>

Journal of Applied Mathematics

fig11

Figure 11

Figure 11: Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes 