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.
2010 AMS SUBJECT CLASSIFICATION:
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.