Theory and Modern Applications
Table 13 Error norms and spectral radius for \(Y(\xi , \eta , t)\) and \(Z(\xi , \eta , t)\) of Example 7 for \(T=0.01\) using regular points
N | Present method | [4] | ||||||
|---|---|---|---|---|---|---|---|---|
dt | Re | \(L_{\infty }\) | \(L_{2}\) | RMS | ρ(M) | CPU time | \(L_{\infty }\) | |
solution of Y | ||||||||
100 | 0.0001 | 1 | 4.85E−05 | 3.20E−05 | 1.28E−05 | 1.00000 | 1.28383 | 2.29E−04 |
100 | 0.005 | 10 | 2.33E−04 | 1.77E−04 | 3.01E−05 | 1.00003 | 0.07259 | 7.23E−05 |
400 | 0.001 | 100 | 6.43E−03 | 2.06E−03 | 1.03E−04 | 1.00030 | 9.37317 | 8.80E−05 |
solution of Z | ||||||||
100 | 0.0001 | 1 | 3.93E−05 | 2.91E−05 | 1.22E−05 | 1.00000 | – | 3.23E−04 |
100 | 0.005 | 10 | 4.64E−04 | 3.50E−04 | 4.23E−05 | 1.00005 | – | 1.03E−04 |
400 | 0.001 | 100 | 6.83E−03 | 2.22E−03 | 1.07E−04 | 1.00034 | – | 1.00E−04 |