Comparison between analytical and MATLAB solution of wave equation using finite difference methods

Abstract

This paper presents a comparative study of the analytical solution and the numerical solution of the one-dimensional wave equation using Finite Difference Methods (FDM) in MATLAB. The wave equation models various physical phenomena, such as vibrations in strings and sound waves. The numerical solutions were obtained using Finite Difference Methods FDM approaches and compared with the analytical solution to evaluate accuracy and stability. The results show that the numerical solution should match the exact solution closely since r=1 ensures stability and accuracy. The maximum error should be very small. The finite difference method is fast for this problem due to its simple time-stepping formula. The elapsed time per run should be minimal.