Table 1 Error estimates and convergence order for the Galerkin-Crank-Nicolson scheme (4.1) to the Eq. (6.4) at \(t=10\)
k | \(\|u^{n}-u_{h}^{n}\|_{\infty}\) | Order | \(\|u^{n}-u_{h}^{n}\|_{\infty}/(h^{2}+k^{2})\) |
|---|---|---|---|
1/10 | 2.8080 × 10−8 | – | 1.4040 × 10−6 |
1/20 | 5.9795 × 10−9 | 2.1670 | 1.1959 × 10−6 |
1/40 | 1.4312 × 10−9 | 2.0440 | 1.1450 × 10−6 |
1/80 | 3.5376 × 10−10 | 2.0114 | 1.1320 × 10−6 |
1/160 | 8.6987 × 10−11 | 2.0166 | 1.1134 × 10−6 |