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Theory and Modern Applications

Table 4 Errors and computational orders of central difference scheme 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)

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

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

8.573e−02

–

4.286e−02

–

0.187456

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

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

1.447e−02

2.57

7.237e−03

2.57

1.381777

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

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

6.001e−03

2.17

3.006e−03

2.17

12.942769

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

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

3.304e−03

2.08

1.652e−03

2.08

53.898653

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

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

2.092e−03

2.05

1.046e−03

2.05

161.459585

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

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

1.445e−03

2.03

7.225e−04

2.03

429.255721