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 9</h2><div class="floats-full-page-caption"><table>Numerical solutions for Example <a href="../../464321/#ex4">5.4</a> with fixed <svg height="13.55" id="M298" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 48.5625 13.55" width="48.5625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<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">8</tspan>
</text>
</g>
</g>
</svg> at time <svg height="10.9125" id="M299" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 47.650002 10.9125" width="47.650002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<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">1</tspan>
<tspan style="font-size: 12.50px; " x="28.63187" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.75762" y="0">0</tspan>
</text>
</g>
</g>
</svg>, and different values of <svg height="13.075" id="M300" style="vertical-align:-1.76814pt" version="1.1" viewbox="0 0 230.2 13.075" width="230.2" 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">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">3</tspan>
<tspan style="font-size: 12.50px; " x="38.184162" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="43.397915" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="49.649414" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="52.775162" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="59.026665" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="64.227913" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="70.479408" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="73.605164" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="79.856659" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="85.070412" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="91.321915" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="94.447662" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="100.69917" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="105.91291" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="112.16441" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="115.29016" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="121.54166" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="126.74291" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="132.99442" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="136.12016" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="142.37166" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="147.58542" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="153.83691" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="156.96266" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="163.21416" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="168.42792" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="174.67941" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="177.80516" 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.009" src="https://static-01.hindawi.com/articles/ijde/volume-2010/464321/figures/464321.fig.009.jpg" /></td></tr></table></div></div>

Figure 9 | Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

title

Figure 9: Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

description

Figure 9

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