Theory and Modern Applications
Table 3 \(L_{\infty }\), \(L_{2}\) and RMS errors for Example 2
(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 | 6.4058(−6) | 1.4539(−5) | 3.3356(−6) | 5.2848(−6) | 2.0991(−5) | 3.3613(−6) |
\(\sqrt{\frac{7}{60}}\) | 1.4202(−4) | 3.5828(−4) | 8.2196(−5) | 1.8686(−4) | 7.2452(−4) | 1.1601(−4) | ||
\(\frac{1}{100}\) | 100 | 6.4058(−6) | 1.4539(−5) | 3.3356(−6) | 5.2848(−6) | 2.0991(−5) | 3.3613(−6) | |
\(\sqrt{\frac{7}{60}}\) | 1.4202(−4) | 3.5828(−4) | 8.2196(−5) | 1.8686(−4) | 7.2452(−4) | 1.1601(−4) | ||
\((30,-30,\frac{1}{12})\) | \(\frac{1}{100}\) | 50 | 9.3013(−6) | 2.1326(−5) | 4.8926(−7) | 3.9930(−6) | 1.5921(−5) | 2.5494(−6) |
\(\sqrt{\frac{7}{60}}\) | 2.4187(−4) | 6.1364(−4) | 1.4078(−4) | 1.4128(−4) | 5.4912(−4) | 8.7930(−5) | ||
\(\frac{1}{100}\) | 100 | 9.3013(−6) | 2.1326(−5) | 4.8926(−7) | 3.9930(−6) | 1.5921(−5) | 2.5494(−6) | |
\(\sqrt{\frac{7}{60}}\) | 2.4187(−4) | 6.1364(−4) | 1.4078(−4) | 1.4128(−4) | 5.4912(−4) | 8.7930(−5) | ||