Analytic numerical solutions with a priori error bounds of initial value problems for the time dependent coefficient wave equation

Abstract

This paper deals with the construction of analytic numerical solutions of initial value problems for the time dependent coefficient wave equation. The proposed analytic numerical approximation is constructed after obtaining an integral expression of the exact solution and further numerical integration. The exact integral expression of the solution is achieved using Fourier transforms and the numerical integration is based on truncation and the composite Simpson rule. Aproximations can be symbolically obtained using Mathematica 4.0. A priori error bounds for the approximation in terms of data problem are given.