Theory and Modern Applications
Table 7 Error norms for Example 1 when \(N=64\) and \(\Delta t=0.001\)
t | α = 0.2 | α = 0.5 | α = 0.8 | |||
|---|---|---|---|---|---|---|
\(L_{\infty}\) | \(L_{2}\) | \(L_{\infty}\) | \(L_{2}\) | \(L_{\infty}\) | \(L_{2}\) | |
0.2 | 7.7931 × 10−8 | 5.3722 × 10−8 | 3.6339 × 10−7 | 2.5744 × 10−7 | 2.1057 × 10−6 | 3.6237 × 10−6 |
0.4 | 4.1594 × 10−7 | 2.8554 × 10−7 | 4.4462 × 10−7 | 3.1036 × 10−7 | 4.7705 × 10−6 | 3.3828 × 10−6 |
0.6 | 1.1898 × 10−6 | 8.1671 × 10−7 | 1.0487 × 10−6 | 7.2256 × 10−7 | 4.8911 × 10−6 | 3.4553 × 10−6 |
0.8 | 2.5164 × 10−6 | 1.7275 × 10−6 | 2.5481 × 10−6 | 1.7497 × 10−6 | 6.1172 × 10−6 | 4.2852 × 10−6 |
1.0 | 4.4909 × 10−6 | 3.0839 × 10−6 | 5.4123 × 10−6 | 3.7133 × 10−6 | 9.4954 × 10−6 | 6.5892 × 10−6 |