Theory and Modern Applications
Table 10 Error norms and spectral radius for \(Y(\xi ,t)\) and \(Z(\xi ,t)\) of Example 5 for \(dt=0.001\)
T | Present method using CGL points | [47] | [48] | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
α | β | ρ(M) | \(L_{\infty }\) | \(L_{2}\) | RMS | \(L_{\infty }\) | \(L_{2}\) | \(L_{\infty }\) | \(L_{2}\) | |
solution of Y | ||||||||||
0.5 | 0.1 | 0.3 | 1.00030 | 2.04E−06 | 1.80E−06 | 1.74E−06 | 4.17E−05 | 6.74E−04 | 9.62E−04 | 3.25E−05 |
0.3 | 0.03 | 1.00003 | 6.45E−06 | 3.66E−06 | 3.54E−06 | 4.59E−05 | 7.33E−04 | 4.31E−04 | 2.73E−05 | |
1 | 0.1 | 0.3 | 1.00077 | 4.03E−06 | 3.53E−06 | 3.41E−06 | 8.26E−05 | 1.33E−03 | 1.15E−03 | 2.41E−05 |
0.3 | 0.03 | 1.00024 | 1.29E−05 | 7.18E−06 | 6.96E−06 | 9.18E−05 | 1.45E−03 | 1.27E−03 | 5.83E−05 | |
solution of Z | ||||||||||
0.5 | 0.1 | 0.3 | 1.00003 | 1.75E−06 | 8.68E−07 | 8.40E−07 | 1.48E−04 | 9.06E−04 | 3.33E−04 | 2.75E−05 |
0.3 | 0.03 | 1.00004 | 1.05E−05 | 8.36E−06 | 8.09E−06 | 5.73E−04 | 1.59E−03 | 1.15E−03 | 2.45E−04 | |
1 | 0.1 | 0.3 | 1.00007 | 3.51E−06 | 1.71E−06 | 1.66E−06 | 4.77E−05 | 1.25E−03 | 1.16E−03 | 3.75E−05 |
0.3 | 0.03 | 1.00002 | 2.10E−05 | 1.64E−05 | 1.59E−05 | 3.62E−04 | 2.25E−03 | 1.64E−03 | 4.53E−04 | |