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Theory and Modern Applications

Table 7 Errors and computational orders of compact difference scheme with \(\beta =10\) for V

From: Compact difference scheme for two-dimensional fourth-order hyperbolic equation

h

τ

\(\|V-v\|_{L^{\infty }}\)

order≈

\(\|V-v\|_{L^{2}}\)

order≈

CPU (s)

\(\frac{1}{10}\)

\(\frac{1}{{10}^{2}}\)

2.711e−07

–

1.367e−07

–

0.315426

\(\frac{1}{20}\)

\(\frac{1}{{20}^{2}}\)

1.347e−08

4.33

9.382e−09

3.87

2.235077

\(\frac{1}{30}\)

\(\frac{1}{{30}^{2}}\)

2.201e−09

4.47

1.691e−09

4.23

16.917521

\(\frac{1}{40}\)

\(\frac{1}{{40}^{2}} \)

6.851e−10

4.01

5.122e−10

4.15

64.900482

\(\frac{1}{50}\)

\(\frac{1}{{50}^{2}}\)

2.889e−10

3.93

2.052e−10

4.10

193.079116

\(\frac{1}{60}\)

\(\frac{1}{{60}^{2}}\)

1.405e−10

3.95

9.756e−11

4.08

494.024067