Compact difference scheme for the two-dimensional semilinear wave equation

Abstract

In this article, we investigate the use of a high-order compact finite difference method for solving a two-dimensional damped semilinear wave equation. We use a new iterative methods that employs compact finite difference operators to approximate the second-order spatial derivatives and achieve fourth-order convergence. We establish the stability and convergence of the compact finite difference scheme in the sense of the discrete H1-norm. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed scheme.