Table 2 The errors for numerical solutions \(u^n\) of the scheme (11)–(14) at different time t with various \(\tau \) when \(h=0.05\)
t | \(\tau =0.1\) | 0.05 | 0.025 | 0.0125 | ||||
|---|---|---|---|---|---|---|---|---|
\(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | \(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | \(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | \(e^n_{\epsilon _1}\) | \(e^n_{\epsilon _2}\) | |
2 | 2.1201e−2 | 3.9697e−2 | 5.4220e−3 | 1.0131e−2 | 1.3673e−3 | 2.5533e−3 | 3.4332e−4 | 6.4146e−4 |
4 | 4.1031e−2 | 7.8091e−2 | 1.0443e−2 | 1.9881e−2 | 2.6281e−3 | 5.0027e−3 | 6.5986e−4 | 1.2555e−3 |
6 | 5.9886e−2 | 1.1514e−1 | 1.5225e−2 | 2.9270e−2 | 3.8276e−3 | 7.3585e−3 | 9.6034e−4 | 1.8457e−3 |
8 | 7.8493e−2 | 1.5154e−1 | 1.9948e−2 | 3.8497e−2 | 5.0129e−3 | 9.6738e−3 | 1.2572e−3 | 2.4257e−3 |
10 | 9.7041e−2 | 1.8768e−1 | 2.4657e−2 | 4.7665e−2 | 6.1945e−3 | 1.1974e−2 | 1.5533e−3 | 3.0020e−3 |