Solution for the nonlinear telegraph equation with two space variables

TL;DR

This paper develops a numerical method combining Laplace transform and Adomian Decomposition to solve the nonlinear telegraph equation with two spatial variables, providing an efficient approach for analytic and approximate solutions.

Contribution

It introduces a novel combined Laplace transform and Adomian Decomposition method for solving nonlinear telegraph equations with two spatial variables.

Findings

The method is easy to implement.

It provides accurate analytic and approximate solutions.

The approach is computationally attractive.

Abstract

In this paper, we consider two space variables of nonlinear telegraph equation in terms of voltage and current. The numerical algorithm based on the Laplace transform method (LDM) is applied to obtain analytic and approximate solutions of the space-time nonlinear telegraph equations. The LDM is combined in the form of Laplace transform and Adomian Decomposition method. The results obtained by the LDM show that the approach is easy to implement and computationally very attractive.