A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients

ABSTRACT

In this paper, a combined compact finite difference method (CCD) together with alternating direction implicit (ADI) scheme is developed for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. The proposed CCD-ADI method is second-order accurate in time variable and sixth-order accurate in space variable. For the linear hyperbolic equation, the CCD-ADI method is shown to be unconditionally stable by using the Von Neumann stability analysis. Numerical results for both linear and nonlinear hyperbolic equations are presented to illustrate the high accuracy of the proposed method.

KEYWORDS:

• Hyperbolic telegraph equation
• combined compact difference scheme
• alternating direction implicit method
• unconditional stability
• variable coefficients

2010 AMS SUBJECT CLASSIFICATION:

• 65M06

Acknowledgements

The author would like to thank two anonymous reviewers for their constructive comments that improved the paper substantially.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Dongdong He was supported by the National Natural Science Foundation of China [No. 11402174], and the president fund-startup research grant from the Chinese University of Hong Kong, Shenzhen. Kejia Pan was supported by the National Natural Science Foundation of China [No. 41474103], the Excellent Youth Foundation of Hunan Province of China [No. 2018JJ1042] and the Innovation-Driven Project of Central South University [No. 2018CX042].