Theory and Modern Applications
Table 1 Absolute error between the exact and numerical solutions of the variable order nonlinear reaction–subdiffusion equation (30) for different values of \(\alpha(x,t) \), Δt and Δx
From: Finite difference approach for variable order reaction–subdiffusion equations
α(x,t) | \(\Delta x=\frac{1}{5}\),\(\Delta t=\frac {1}{25}\) | \(\Delta x=\frac{1}{10}\) ,\(\Delta t=\frac{1}{100}\) | \(\Delta x=\frac{1}{20}\),\(\Delta t=\frac{1}{400}\) |
|---|---|---|---|
\(e^{xt-5}\) | 5.449 × 10−3 | 2.604 × 10−3 | 8.085 × 10−4 |
[33] | 3.9838 × 10−3 | 1.0056 × 10−3 | 4.5969 × 10−4 |
\(\frac{10-(xt)^{2}}{300}\) | 5.585 × 10−3 | 2.776 × 10−3 | 8.532 × 10−4 |
[33] | 4.0042 × 10−3 | 1.0109 × 10−3 | 4.3241 × 10−4 |
\(\frac{15-x^{2}+t^{4}}{400}\) | 5.594 × 10−3 | 2.791 × 10−3 | 8.566 × 10−4 |
[33] | 4.0025 × 10−3 | 1.0093 × 10−3 | 4.2750 × 10−4 |
\(\frac{15+\cos(xt)}{300}\) | 5.672 × 10−3 | 2.912 × 10−3 | 8.881 × 10−4 |
[33] | 4.0133 × 10−3 | 1.0128 × 10−3 | 4.1130 × 10−4 |
\(\frac{5^{xt}-\cos(xt)}{40}\) | 5.341 × 10−3 | 2.598 × 10−3 | 8.018 × 10−4 |
[33] | 3.9431 × 10−3 | 9.9547 × 10−3 | 4.3483 × 10−4 |
\(\frac{e^{xt}+\sin(xt)}{50}\) | 5.451 × 10−3 | 2.728 × 10−3 | 8.356 × 10−4 |
[33] | 3.9715 × 10−3 | 1.0019 × 10−3 | 4.2391 × 10−4 |
\(\frac{10-\sin^{3}(xt)}{300}\) | 5.583 × 10−3 | 2.776 × 10−3 | 8.532 × 10−4 |
[33] | 4.0037 × 10−3 | 1.0103 × 10−3 | 4.3143 × 10−4 |
\(\frac{25-x^{4}+\sin ^{3}(t)}{500}\) | 5.653 × 10−3 | 2.881 × 10−3 | 8.794 × 10−4 |
[33] | 4.0097 × 10−3 | 1.0118 × 10−3 | 4.1491 × 10−4 |
\(\frac{20-\sin^{3}(x)+\cos^{5}(t)}{400}\) | 5.668 × 10−3 | 2.898 × 10−3 | 8.843 × 10−4 |
[33] | 4.0148 × 10−3 | 1.0132 × 10−3 | 4.1486 × 10−4 |