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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 12 Errors and computational orders of central difference scheme with \(\beta =\frac{1}{10}\) for V

h	τ	\(\\|V-v\\|_{L^{\infty }}\)	order≈	\(\\|V-v\\|_{L^{2}}\)	order≈	CPU (s)
\(\frac{1}{10}\)	\(\frac{1}{{10}^{2}}\)	2.112	–	5.087e−01	–	0.242853
\(\frac{1}{20}\)	\(\frac{1}{{20}^{2}}\)	5.117e−01	2.04	1.234e−01	2.05	1.429410
\(\frac{1}{30}\)	\(\frac{1}{{30}^{2}}\)	2.261e−01	2.01	5.455e−02	2.01	13.395006
\(\frac{1}{40}\)	\(\frac{1}{{40}^{2}} \)	1.270e−01	2.01	3.063e−02	2.01	53.665479
\(\frac{1}{50}\)	\(\frac{1}{{50}^{2}}\)	8.118e−02	2.00	1.959e−02	2.00	160.600921
\(\frac{1}{60}\)	\(\frac{1}{{60}^{2}}\)	5.635e−02	2.00	1.360e−02	2.00	411.886623