Theory and Modern Applications
Table 1 The errors for different 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 |
|---|---|---|---|---|---|---|
(1/8000,1/10) | \(2.0642e^{-4}\) | Â | \(7.0170e^{-3}\) | Â | \(4.3022e^{-1}\) | Â |
(1/8000,1/20) | \(1.4750e^{-5}\) | 4.1349 | \(8.1325e^{-4}\) | 3.1091 | \(1.0389e^{-1}\) | 2.0500 |
(1/8000,1/40) | \(7.1398e^{-7}\) | 4.0406 | \(9.9680e^{-5}\) | 3.0283 | \(2.5745e^{-2}\) | 2.0127 |
(1/8000,1/80) | \(4.1614e^{-8}\) | 4.1614 | \(1.2399e^{-5}\) | 3.0071 | \(6.4221e^{-3}\) | 2.0032 |