One-Dimensional Wave Equation Computation

The one-dimensional wave equation computation program serves as a highly valuable numerical analysis tool. This implementation utilizes the finite difference method, employing central difference approximations for both spatial and temporal derivatives to discretize the wave equation. The core algorithm typically involves time-stepping schemes like the explicit Euler method or leapfrog method, with stability conditions governed by the Courant-Friedrichs-Lewy (CFL) criterion. The program can effectively simulate various wave phenomena including acoustic waves and seismic waves through parameter adjustments in the wave speed and boundary conditions. Furthermore, by modifying the governing equations and implementing appropriate numerical schemes, the program can be adapted for broader applications such as optical wave propagation and electromagnetic wave analysis in electronics. Key functions include boundary condition handling (Dirichlet, Neumann, or absorbing boundaries), initial condition setup, and wave propagation visualization. For researchers and engineers working with wave-related computations, this program provides an essential framework with customizable parameters and extensible architecture.