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Theory and Modern Applications

Table 5 Errors and computational orders of compact difference scheme with \(\beta =10\) for W

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

h

τ

\(\|W-w\|_{L^{\infty }}\)

order≈

\(\|W-w\|_{L^{2}}\)

order≈

CPU (s)

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

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

5.803e−07

–

3.316e−07

–

0.315426

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

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

4.149e−08

3.81

1.840e−08

4.17

2.235077

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

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

7.796e−09

4.12

3.417e−09

4.15

16.917521

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

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

2.358e−09

4.16

1.046e−09

4.11

64.900482

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

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

9.320e−10

4.16

4.199e−10

4.10

193.079116

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

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

4.528e−10

3.96

1.998e−10

4.07

494.024067