Theory and Modern Applications
Table 1 \(L_{\infty }\), \(L_{2}\) and RMS errors for Example 1
(p,q,σ) | r | Time steps | \(h=\frac{1}{20}\) | \(h=\frac{1}{40}\) | ||||
|---|---|---|---|---|---|---|---|---|
\(L_{\infty }\) | \(L_{2}\) | RMS | \(L_{\infty }\) | \(L_{2}\) | RMS | |||
\((25,-25,\frac{1}{12})\) | \(\frac{1}{100}\) | 50 | 1.0462(−6) | 2.7700(−6) | 6.3549(−7) | 5.8011(−7) | 2.5112(−6) | 4.0211(−7) |
\(\sqrt{\frac{7}{60}}\) | 3.5860(−5) | 1.0775(−4) | 2.4719(−5) | 1.9822(−5) | 8.7003(−5) | 1.3932(−5) | ||
\(\frac{1}{100}\) | 100 | 1.0462(−6) | 2.7704(−6) | 6.3557(−7) | 5.8012(−7) | 2.5112(−6) | 4.0211(−7) | |
\(\sqrt{\frac{7}{60}}\) | 3.5989(−5) | 1.0815(−4) | 2.4810(−5) | 1.9823(−5) | 8.7044(−5) | 1.3938(−5) | ||
\((30,-30,\frac{1}{12})\) | \(\frac{1}{100}\) | 50 | 8.4689(−7) | 2.1899(−6) | 5.0240(−7) | 4.8030(−7) | 2.0718(−6) | 3.3175(−7) |
\(\sqrt{\frac{7}{60}}\) | 2.9030(−5) | 8.7176(−5) | 1.9999(−5) | 1.6412(−5) | 7.2067(−5) | 1.1540(−5) | ||
\(\frac{1}{100}\) | 100 | 8.4699(−7) | 2.1902(−6) | 5.0246(−7) | 4.8031(−7) | 2.0718(−6) | 3.3175(−7) | |
\(\sqrt{\frac{7}{60}}\) | 2.9134(−5) | 8.7499(−5) | 2.0074(−5) | 1.6420(−5) | 7.2101(−5) | 1.1545(−5) | ||