Numerical Solution of Second Order One Dimensional Linear Hyperbolic Telegraph Equation

Abstract

In this paper, the numerical solution of second order one dimensional linear hyperbolic telegraph equation using crank Nicholson and fourth order stable centeral difference methods have been presented. First, the given domain is discretized and the derivatives of the differential equation were replaced by finite difference approximations and then, transformed to system of equations that can be solved by matrix inverse method. The stability and consistency of the method are established. To validate the applicability of the method, model examples have been considered and solved for different mesh sizes. As it can be observed from the numerical results presented in Tables and graphs, the present method approximates the exact solution very well.

Key words: Hyperbolic Telegraph equation, numerical solution and convergence of method