Theory and Modern Applications
Table 6 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{100}\), \(\beta =2\) and \(\alpha =0.3\) at \(T=1\) for Example 2
h | \(\|u^{n}-u_{h}^{n}\|\) | Rate | \(\|u^{n}-u_{h}^{n}\|_{1}\) | Rate | \(\|I_{h}u^{n}-u_{h}^{n}\|_{1}\) | Rate | \(\|u^{n}-\varPi _{2h}u_{h}^{n}\|_{1}\) | Rate |
|---|---|---|---|---|---|---|---|---|
π/4 | 2.7064e-1 | 1.96 | 6.4016e-1 | 0.98 | 7.6732e-2 | 2.18 | 6.2915e-2 | 2.00 |
π/8 | 6.9390e-2 | 1.99 | 3.2374e-1 | 1.00 | 1.6960e-2 | 2.05 | 1.5732e-2 | 1.97 |
π/16 | 1.7445e-2 | 2.00 | 1.6238e-1 | 1.00 | 4.0926e-3 | 2.02 | 4.0023e-3 | 2.00 |
π/32 | 4.3629e-3 | 2.01 | 8.1255e-2 | 1.00 | 1.0084e-3 | 2.04 | 1.0024e-3 | 2.03 |
π/64 | 1.0865e-3 | ∗ | 4.0636e-2 | ∗ | 2.4562e-4 | ∗ | 2.4523e-4 | ∗ |