Theory and Modern Applications
Table 3 Error, energy and momentum for Problem 2 using FDS-S
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 | 1.02626203 | 3.6∗10−6 | 0.69289524 | 2.9∗10−5 | ||
0.2 | 1.02895892 | 4.0∗10−7 | 0.69512790 | 1.4∗10−6 | ||
0.1 | 1.1∗10−2 | 2.00 | 1.02964231 | 7.5∗10−8 | 0.69569642 | 1.4∗10−8 |
0.05 | 2.6∗10−3 | 2.00 | 1.02981375 | 1.7∗10−8 | 0.69583920 | 2.7∗10−8 |
0.025 | 6.6∗10−4 | 2.00 | 1.02985665 | 4.2∗10−9 | 0.69587494 | 8.1∗10−9 |
0.0125 | 1.6∗10−4 | 2.00 | 1.02986738 | 1.0∗10−9 | 0.69588387 | 2.1∗10−9 |
0.00625 | 4.1∗10−5 | 2.00 | 1.02987006 | 3.1∗10−10 | 0.69588611 | 4.9∗10−10 |