Numerical solution of second order one dimensional linear hyperbolic telegraph equation

Abstract

In this study, the numerical solution of second order one dimensional linear hyperbolic telegraph equations using crank Nicholson and stable finite difference method have been presented. First, the given domain or region is discritized and the derivatives of the differential equation were replaced by finite difference approximations and then, transformed to system of equations which can be solved by matrix inverse method. The stability and consistency of the method are established which shows convergence of the method. To validate the applicability of the method, model examples have been considered and solved at 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.