Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

<div class="floats-full-page floats-full-page-figure"><h2>Figure 7</h2><div class="floats-full-page-caption"><table>Numerical solutions for Example <a href="../../464321/#ex3">5.3</a> with <svg height="11.1" id="M276" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 47.862499 11.1" width="47.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.806911" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.932661" y="0">5</tspan>
</text>
</g>
</g>
</svg> and <svg height="13.7375" id="M277" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 48.5625 13.7375" width="48.5625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.7375)">
<g transform="translate(72,-61.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜇</tspan>
<tspan style="font-size: 12.50px; " x="11.077658" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="23.118048" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="29.369547" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="32.495296" y="0">5</tspan>
</text>
</g>
</g>
</svg> at different times <svg height="13.075" id="M278" style="vertical-align:-1.76814pt" version="1.1" viewbox="0 0 99.737503 13.075" width="99.737503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.075)">
<g transform="translate(72,-61.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.63187" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.75762" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="38.009121" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="43.22287" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="49.474373" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="52.600121" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="58.85162" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="64.052872" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="70.304367" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="73.430122" y="0">0</tspan>
</text>
</g>
</g>
</svg>.</table></div><div class="floats-full-page-content"><table class="table-group" width="800px"><tr class="fig-image"><td><img alt="464321.fig.007" src="https://static-01.hindawi.com/articles/ijde/volume-2010/464321/figures/464321.fig.007.jpg" /></td></tr></table></div></div>

Figure 7 | Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

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Figure 7: Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

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Figure 7

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