Table 2 The errors for different time step Ît at \(t=1\) and convergence orders
(Ît,h) | \(\|u-u_{h}\|\) | rate | \(\|u-u_{h}\|_{1}\) | rate | \(\|u-u_{h}\|_{2} \) | rate |
|---|---|---|---|---|---|---|
(1/20,1/1000) | \(1.3225e^{-3}\) | Â | \(4.7367e^{-3}\) | Â | \(2.9876e^{-2}\) | Â |
(1/40,1/1000) | \(3.4476e^{-4}\) | 1.9396 | \(1.2381e^{-3}\) | 1.9357 | \(7.7977e^{-3}\) | 1.9379 |
(1/80,1/1000) | \(8.6004e^{-5}\) | 2.0031 | \(3.1124e^{-4}\) | 1.9920 | \(1.9581e^{-3}\) | 1.9936 |
(1/160,1/1000) | \(2.1555e^{-5}\) | 1.9964 | \(7.8398e^{-5}\) | 1.9892 | 4.9482â4 | 1.9845 |