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

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 inL2- andH1-norms by the discrete energy method. Numerical experiments are provided to demonstrate the accuracy and efficiency of the schemes. [ABSTRACT FROM AUTHOR]