Numerical Solution of Telegraph Equation by Using LT Inversion Technique

Abstract

In this paper, the numerical solution of one-dimensional linear hyperbolic telegraph equation, which describe wave propagation of electric signals in a cable transmission line, is proposed employing the well known homotopy perturbation method (HPM) and laplace transform(LT). Using Laplace transform scheme, the problem is converted into a partial differential equation without any differentiation respect to time. Homotopy perturbation method is applied in the Laplace transform domain. We use Stehfest's numerical inversion algorithm of Laplace transform to retrieve the time domain solution. The performance was found to be very good. The approximate solutions are in excellent agreement with those by the Chebyshev spectral collocation method (CSCM) and  the method uses interpolating scaling functions. To illustrate the method some examples are provided. The results show the simplicity and the efficiency of the method.