Numerical Solution Of 1-D And 2-D Wave Equations Using Finite Difference Methods

Abstract

This study focuses on applications of finite difference methods for solving 1D and 2D wave equations. Explicit and implicit finite different schemes based on domain discretization are analysed for 1D wave equation. We also considered explicit scheme for 2D wave equation. The partial differential equations are replaced by difference equations at the interior nodal points (meshes) and systems of algebraic equation are solved numerically. We also investigate how the space and time step sizes affect the stability, convergence and consistency of explicit FDM in one dimensional and two dimensional wave equations. We finally present test examples and show the results using math lab codes.