Theory and Modern Applications
Table 11 Errors and computational orders of compact difference scheme with \(\beta =\frac{1}{10}\) for V
From: Compact difference scheme for two-dimensional fourth-order hyperbolic equation
h | Ï | \(\|V-v\|_{L^{\infty }}\) | orderâ | \(\|V-v\|_{L^{2}}\) | orderâ | CPU (s) |
|---|---|---|---|---|---|---|
\(\frac{1}{10}\) | \(\frac{1}{{10}^{2}}\) | 9.674eâ02 | â | 2.651eâ02 | â | 0.330710 |
\(\frac{1}{20}\) | \(\frac{1}{{20}^{2}}\) | 5.744eâ03 | 4.07 | 1.572eâ03 | 4.08 | 3.542983 |
\(\frac{1}{30}\) | \(\frac{1}{{30}^{2}}\) | 1.130eâ03 | 4.01 | 3.094eâ04 | 4.01 | 18.320414 |
\(\frac{1}{40}\) | \(\frac{1}{{40}^{2}} \) | 3.570eâ04 | 4.01 | 9.772eâ05 | 4.01 | 68.516085 |
\(\frac{1}{50}\) | \(\frac{1}{{50}^{2}}\) | 1.461eâ04 | 4.00 | 3.999eâ05 | 4.00 | 221.163513 |
\(\frac{1}{60}\) | \(\frac{1}{{60}^{2}}\) | 7.040eâ05 | 4.00 | 1.928eâ05 | 4.00 | 540.818697 |