Theory and Modern Applications
Table 4 Error, energy and momentum for Problem 2 using FDS-M
From: Invariant preserving schemes for double dispersion equations
h = τ | Error | Energy | Momentum | |||
|---|---|---|---|---|---|---|
\(\psi _{h}\) | κ | \(H_{h}^{ {K}}\) | \(|H_{h}^{0}-H_{h}^{K}|\) | \(M_{h}^{ {K}}\) | \(|M_{h}^{0}-M_{h}^{K}|\) | |
0.4 | 1.02593880 | 1.7∗10−4 | 0.69286589 | 2.8∗10−13 | ||
0.2 | 1.02893447 | 1.4∗10−5 | 0.69512648 | 2.9∗10−13 | ||
0.1 | 4.0∗10−2 | 1.92 | 1.02964003 | 1.6∗10−6 | 0.69569643 | 2.9∗10−13 |
0.05 | 1.1∗10−2 | 1.98 | 1.02981343 | 2.7∗10−7 | 0.69583923 | 3.8∗10−13 |
0.025 | 2.7∗10−3 | 1.99 | 1.02985658 | 6.0∗10−8 | 0.69587494 | 2.1∗10−12 |
0.0125 | 6.7∗10−4 | 2.00 | 1.02986736 | 1.4∗10−8 | 0.69588388 | 7.5∗10−12 |
0.00625 | 1.7∗10−4 | 2.00 | 1.02987005 | 3.5∗10−9 | 0.69588611 | 3.7∗10−11 |