Theory and Modern Applications
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) |
---|---|---|---|---|---|---|
\(\frac{1}{10}\) | \(\frac{1}{{10}^{2}}\) | 2.711eâ07 | â | 1.367eâ07 | â | 0.315426 |
\(\frac{1}{20}\) | \(\frac{1}{{20}^{2}}\) | 1.347eâ08 | 4.33 | 9.382eâ09 | 3.87 | 2.235077 |
\(\frac{1}{30}\) | \(\frac{1}{{30}^{2}}\) | 2.201eâ09 | 4.47 | 1.691eâ09 | 4.23 | 16.917521 |
\(\frac{1}{40}\) | \(\frac{1}{{40}^{2}} \) | 6.851eâ10 | 4.01 | 5.122eâ10 | 4.15 | 64.900482 |
\(\frac{1}{50}\) | \(\frac{1}{{50}^{2}}\) | 2.889eâ10 | 3.93 | 2.052eâ10 | 4.10 | 193.079116 |
\(\frac{1}{60}\) | \(\frac{1}{{60}^{2}}\) | 1.405eâ10 | 3.95 | 9.756eâ11 | 4.08 | 494.024067 |