An Efficient Approach to Approximate Analytical Solutions of Second-Order Nonlinear Telegraph Equations

Abstract

We propose the Multistep Modified Reduced Differential Transform Method (MMRDTM) as a novel approach to solving Nonlinear Telegraph Equations (NLTEs). To streamline the process, we replace the nonlinear terms within NLTEs with corresponding Adomian polynomials before implementing the multistep technique. This substitution simplifies the solution process and enables more precise approximations over longer time domains. To validate the MMRDTM's efficacy and accuracy, we solve two different NLTE problems, showcasing the method's capability for analytical approximation. The resulting outcomes are then presented both in tabular and graphical formats. The findings confirm that MMRDTM delivers highly accurate, and in some cases, exact solutions for the studied equations.