MATLAB Program for Solving Wave Equation Using Finite Difference Method

The following presents MATLAB program code for solving wave equations using finite difference methods. Finite difference methods are commonly employed to approximate solutions for partial differential equations, particularly when analytical solutions are unavailable or difficult to obtain. In this implementation, we discretize the wave equation into a system of algebraic equations using finite difference schemes and solve them numerically to obtain approximate solutions for wave propagation problems. This program implementation involves the following key algorithmic steps: 1. Define spatial computational domain and temporal discretization parameters 2. Specify initial conditions and boundary constraints for wave propagation 3. Apply central difference schemes to discretize the wave equation's spatial and temporal derivatives 4. Solve the resulting system of algebraic equations using time-stepping algorithms 5. Implement visualization routines to analyze wave propagation behavior and solution accuracy The core implementation utilizes MATLAB's vectorization capabilities for efficient computation, with specific attention to stability conditions (such as Courant-Friedrichs-Lewy condition) and boundary handling mechanisms. The program structure ensures proper handling of wave equation parameters including wave speed, domain dimensions, and discretization intervals. Below is the structured program code: