A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

Abstract

In this paper we investigate approximate analytical solution so called voltage in one and two space variables for linear and nonlinear telegraph equations by a reliable method namely Modified Laplace Decomposition Method (MLDM) using MATLAB and MATHEMATICA software tools. The MLDM is a mixture of Laplace transform with modified Adomian decomposition method based on Newton Raphson method. The nonlinearity of the problem is tackled by Adomian decomposition and approximate analytical solution to the partial differential equation handled by using the Laplace and inverse Laplace transform technique without differentiation in time domain. We use Newton Raphson method in the domain of Adomian polynomial to modify it. Theoretical concepts for the approximate analytical solution of present scheme are well behaved through stability and convergence analysis. Five numerical examples are carried out in order to check the effectiveness and applicability of the proposed scheme. The telegraph equation with one space variable is solved numerically whereas the approximate analytical solution obtained for two space variables. Employing MLDM, it is possible to obtain the approximate analytical solution (i.e., voltage) of a telegraph equation and found to be in good agreement with exact solutions and also compared with earlier studies for one space variable.