A Finite Point Method for Solving the Time Fractional Richards’ Equation

<table class="table-group" id="tab8"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Time step</td><td class="align_center"><i>ε</i>1</td><td class="align_center">Covergence rate</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">1/10</td><td class="align_center">1.8574<i>e</i> − 04</td><td class="align_left"> </td></tr><tr><td class="align_left">1/20</td><td class="align_center">1.0418<i>e</i> − 04</td><td class="align_center">0.8342</td></tr><tr><td class="align_left">1/40</td><td class="align_center">5.7024<i>e</i> − 05</td><td class="align_center">0.8694</td></tr><tr><td class="align_left">1/80</td><td class="align_center">2.7958<i>e</i> − 05</td><td class="align_center">1.0283</td></tr><tr><td class="align_left">1/160</td><td class="align_center">1.3560<i>e</i> − 05</td><td class="align_center">1.0440</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div><i>ε</i>1 errors and convergence order of numerical solution, when <i>α</i> = 0.8 and the number of nodes is 21 × 21.</div>

Mathematical Problems in Engineering

tab8

Table 8

Table 8: A Finite Point Method for Solving the Time Fractional Richards’ Equation 