Table 1 The errors for numerical solutions \(u^n\) of the scheme (11)–(14) at different time t with various h and \(\tau =h^2\)
t | \(h=0.2\) | 0.1 | 0.05 | 0.025 | ||||
|---|---|---|---|---|---|---|---|---|
\(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | \(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | \(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | \(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | |
2 | 3.7504e−3 | 6.8705e−3 | 2.3827e−4 | 4.3361e−4 | 1.4930e−5 | 2.7153e−5 | 9.3409e−7 | 1.6997e−6 |
4 | 7.1325e−3 | 1.3403e−2 | 4.5011e−4 | 8.438e−4 | 2.8167e−5 | 5.2812e−5 | 1.7639e−6 | 3.3089e−6 |
6 | 1.0303e−2 | 1.9666e−2 | 6.5000e−4 | 1.2367e−3 | 4.0665e−5 | 7.7372e−5 | 2.5487e−6 | 4.8528e−6 |
8 | 1.3432e−2 | 2.5820e−2 | 8.4767e−4 | 1.6227e−3 | 5.3023e−5 | 1.0151e−4 | 3.3268e−6 | 6.3733e−6 |
10 | 1.6551e−2 | 3.1935e−2 | 1.0447e−3 | 2.0063e−3 | 6.5345e−5 | 1.2549e−4 | 4.1045e−6 | 7.8878e−6 |