Theory and Modern Applications
Table 3 Comparison of the \(\pmb{L^{\infty}}\) errors \(\pmb{\max_{0\leq n\leq N}\| u_{h}^{n}-u^{n}\|_{\infty}}\) with \(\pmb{h=\pi/200}\)
α | 1/ τ | Error [ 24 ] | Cvge | Error ( 14 ) | Cvge |
|---|---|---|---|---|---|
1.3 | 10 | 1.897E-02 | - | 2.029E-02 | - |
20 | 5.674E-03 | 1.7413 | 5.487E-03 | 1.8868 | |
40 | 1.702E-03 | 1.7372 | 1.427E-03 | 1.9434 | |
80 | 5.133E-04 | 1.7293 | 3.626E-04 | 1.9763 | |
160 | 1.566E-04 | 1.7131 | 8.981E-05 | 2.0133 | |
1.5 | 10 | 3.911E-02 | - | 1.659E-02 | - |
20 | 1.356E-02 | 1.5286 | 4.509E-03 | 1.8792 | |
40 | 4.720E-03 | 1.5221 | 1.179E-03 | 1.9358 | |
80 | 1.650E-03 | 1.5164 | 3.010E-04 | 1.9692 | |
160 | 5.792E-04 | 1.5102 | 7.496E-05 | 2.0055 | |
1.7 | 10 | 7.908E-02 | - | 1.202E-02 | - |
20 | 3.162E-02 | 1.3225 | 3.283E-03 | 1.8718 | |
40 | 1.274E-02 | 1.3120 | 8.648E-04 | 1.9245 | |
80 | 5.148E-03 | 1.3068 | 2.229E-04 | 1.9561 | |
160 | 2.085E-03 | 1.3037 | 5.604E-05 | 1.9918 |