Theory and Modern Applications
Table 3 The errors for different time step Ît and space step h at \(t=1\) and convergence orders
(Ît,h) | \(\|u-u_{h}\|\) | rate | \(\|u-u_{h}\|_{1}\) | rate | \(\|u-u_{h}\|_{2} \) | rate |
|---|---|---|---|---|---|---|
(1/100,1/10) | \(1.8855e^{-4}\) | Â | \(7.0332e^{-3}\) | Â | \(4.3020e^{-1}\) | Â |
(1/400,1/20) | \(1.0720e^{-5}\) | 4.1366 | \(8.1374e^{-4}\) | 3.1116 | \(1.0389e^{-1}\) | 2.0500 |
(1/1600,1/40) | \(6.5496e^{-7}\) | 4.0327 | 9.9694â5 | 3.0290 | \(2.5745e^{-2}\) | 2.0127 |
(1/6400,1/80) | \(4.0685e^{-8}\) | 4.0088 | \(1.2399e^{-5}\) | 3.0073 | \(6.4221e^{-3}\) | 2.0032 |