Compact alternating direction implicit method to solve two-dimensional nonlinear delay hyperbolic differential equations

Abstract

In this article, a high-order compact alternating direction implicit method combined with a Richardson extrapolation technique is developed to solve a class of two-dimensional nonlinear delay hyperbolic differential equations. The solvability, stability and convergence of the method are analysed simultaneously in L²- and H¹-norms by the discrete energy method. Numerical experiments are provided to demonstrate the accuracy and efficiency of the schemes.

Keywords:

• delay hyperbolic differential equations
• compact alternating direction implicit scheme
• Richardson extrapolation
• solvability
• stability
• convergence

2010 AMS Subject Classifications:

• 65M06
• 65M12
• 65M15

Acknowledgements

We are deeply grateful to the anonymous referees, Editor and Editor-in-Chief Dr Qin Sheng for their insightful comments and helpful suggestions, which have greatly improved the article. This work is supported by NSFC (Grant No. 11171125, 91130003), HSF (Grant No. 2011CDB289) and DSRF of NHU (No. 01-18-011001).