Theory and Modern Applications
Table 1 The error for different space step h at \({t=1}\)
(Δt,h) | \(\Vert u-u_{h} \Vert \) | Rate | \(\Vert u-u_{h} \Vert _{1}\) | Rate | \(\Vert u-u_{h} \Vert _{2} \) | Rate |
|---|---|---|---|---|---|---|
(1/200,000,1/10) | \(2.6858e^{-4}\) | Â | \(7.1462e^{-3}\) | Â | \(4.3020e^{-1}\) | Â |
(1/200,000,1/20) | \(1.2314e^{-5}\) | 4.4470 | \(8.1328e^{-4}\) | 3.1354 | \(1.0389e^{-1}\) | 2.0500 |
(1/200,000,1/40) | \(7.4241e^{-7}\) | 4.0519 | \(9.9745e^{-5}\) | 3.0274 | \(2.5745e^{-2}\) | 2.0127 |
(1/200,000,1/80) | \(4.1905e^{-8}\) | 4.1470 | \(1.2399e^{-5}\) | 3.0080 | \(6.4221e^{-3}\) | 2.0032 |