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-other"><h2>Table 1</h2><div class="floats-full-page-caption">Maximum error behavior versus grid size reduction for Example <a href="../../464321/#ex1">5.1</a> at <svg height="10.9125" id="M215" 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>.</div><div class="floats-full-page-content"><table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr /></td></tr><tr class="thead"><td align="left"><span style="width: 36.537498px;"><svg height="10.95" id="M216" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 36.537498 10.95" width="36.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="10.677562" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">𝜏</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> Maximum error</td></tr><tr><td class="thead-hr" colspan="2"><hr /></td></tr><tr><td align="left"><span style="width: 27.9125px;"><svg height="10.9125" id="M217" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.9125 10.9125" width="27.9125" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="15.978834" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 4.8148E-2</td></tr><tr><td align="left"><span style="width: 27.9125px;"><svg height="10.9125" id="M218" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.9125 10.9125" width="27.9125" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="15.978834" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 1.0111E-2</td></tr><tr><td align="left"><span style="width: 27.9125px;"><svg height="10.9125" id="M219" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.9125 10.9125" width="27.9125" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="15.978834" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 2.0587E-3</td></tr><tr><td align="left"><span style="width: 27.9125px;"><svg height="10.9125" id="M220" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.9125 10.9125" width="27.9125" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="15.978834" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"> 7.3019E-4</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 1 | Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

title

Table 1: Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

description

Table 1

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