Solving damped wave equation using finite difference method and interpolation using cubic B-spline

Abstract

Damped wave equations have been used particularly in the natural sciences and engineering disciplines. The purpose of this study is to apply the technique of finite difference and cubic B-spline interpolation to solve one dimensional damped wave equation with Dirichlet boundary conditions. In this study, the accuracy of numerical methods are compared with exact solution by computing their absolute error and relative error. The computational experiments are conducted using Matlab 2008 and visualisation using Microsoft Excel 2010. As the result, finite difference method and cubic B-spline interpolation are found to give good approximation in solving damped wave equation. In addition, the smaller time step size, T gives better approximations for both finite difference and cubic B-spline interpolation.