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.