1. Compact difference scheme for the two-dimensional semilinear wave equation.
- Author
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M. Aloraini, Najla and Achouri, Talha
- Subjects
- *
FINITE differences , *FINITE difference method , *DIFFERENCE operators , *NONLINEAR differential equations , *PARTIAL differential equations - 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 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]
- Published
- 2024
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