Approximate Solutions for Coupled Systems of Nonlinear PDEs Using the Reduced Differential Transform Method

Mahmoud Rawashdeh

doi:10.3390/mca19020161

Abstract

In this paper, we are concerned with finding approximate solutions to systems of nonlinear PDEs using the Reduced Differential Transform Method (RDTM). We examine this method to obtain approximate numerical solutions for two different types of systems of nonlinear partial differential equations, such as the two- component KdV evolutionary system of order two and the Broer-Kaup (BK) system of equations. The theoretical analysis of the RDTM is investigated for these systems of equations and is calculated in the form of power series with easily computable terms. Illustrative examples will be presented to support the proposed analysis.

Highlights

The Reduced Differential Transform Method [1, 2, 3], was first introduced by Keskin to solve linear and nonlinear PDEs that appears in many Mathematical Physics and engineering applications
Many numerical methods were used in the past to solve systems of nonlinear partial differential equations, such as, Adomian Decomposition Method (ADM) [7, 8], Differential Transform Method (DTM) [9], the Tanh-Coth Method [10], and the Variational Iteration Method (VIM) [11] and others
We successfully found approximate solutions for both systems of nonlinear PDEs by first applying the Reduced Differential Transform Method (RDTM) to both physical models

Summary

INTRODUCTION

The Reduced Differential Transform Method [1, 2, 3], was first introduced by Keskin to solve linear and nonlinear PDEs that appears in many Mathematical Physics and engineering applications. The goal of our study is to use the RDTM to find approximate solutions to two different types of systems of nonlinear partial differential equations and to show how accurate and efficient is the method in finding approximate solutions to other complicated systems of nonlinear partial differential equations. Keskin, in his PhD thesis [3], introduced the reduced form of the differential transform method (DTM) as a reduced differential transform method (RDTM). Abdou [14] finds numerical solutions to the coupled MKdV system of equations and the coupled Schrodinger-KdV system of equations

ANALYSIS OF THE RDTM

Examples

CONCLUSION