Theory and Modern Applications
Table 1 \(\pmb{L_{\infty}}\) -errors for different time steps at \(\pmb{x=\frac{\pi }{4}}\) , \(\pmb{y=\frac{\pi}{4}}\)
From: Fourier pseudo-spectral method for the extended Fisher-Kolmogorov equation in two dimensions
h | Ï„ | \(\boldsymbol{\operatorname {err}(\frac{\pi}{4}, \frac{\pi}{4}, \tau)}\) | \(\boldsymbol{\frac {\operatorname{err}(\frac{\pi}{4}, \frac{\pi}{4}, \tau)}{\tau}}\) | \(\boldsymbol{\frac{\operatorname{err}(\frac{\pi}{4}, \frac{\pi}{4}, \tau )}{\tau^{2}}}\) |
|---|---|---|---|---|
0.0785 | 0.1000 | \(3.700\times\mathrm{e}^{-3}\) | \(3.700\times\mathrm {e}^{-2}\) | 0.3700 |
0.0785 | 0.0500 | \(8.8290\times\mathrm{e}^{-4}\) | \(1.7658\times\mathrm {e}^{-2}\) | 0.3532 |
0.0785 | 0.0250 | \(2.1024\times\mathrm{e}^{-4}\) | \(8.40963\times \mathrm{e}^{-3}\) | 0.3364 |
0.0785 | 0.0125 | \(4.1957\times\mathrm{e}^{-5}\) | \(3.3566\times\mathrm {e}^{-3}\) | 0.2685 |
0.0785 | 0.0080 | \(1.0873\times\mathrm{e}^{-5}\) | \(1.3048\times\mathrm {e}^{-3}\) | 0.1566 |