Numerical Solution of Second Order One Dimensional Linear Hyperbolic Telegraph Equation

Abstract

In this paper, the numerical solution of second order one dimensional linear hyperbolictelegraph equation using crank Nicholson and fourth order stable centeral differencemethods have been presented. First, the given domain is discretized and the derivativesof the differential equation were replaced by finite difference approximations and then,transformed to system of equations that can be solved by matrix inverse method. Thestability and consistency of the method are established. To validate the applicability ofthe 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, thepresent method approximates the exact solution very well.