Compact difference scheme for the two-dimensional semilinear wave equation.

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 method 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 H 1 -norm. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]