Applied Sumudu Transform with Adomian Decomposition Method to the Coupled Drinfeld–Sokolov–Wilson System

Abdulghafor Al-Rozbayani,Ammar Ali

doi:10.33899/csmj.2021.170017

Abdulghafor Al-Rozbayani, Ammar Ali

Open Access

https://doi.org/10.33899/csmj.2021.170017

Copy DOI

Abstract

In this paper, we studied and applied a modern numerical method, which is combining Sumudu transform with Adomian decomposition Method to obtain approximate solutions of the nonlinear the Coupled Drinfeld– Sokolov–Wilson (DSW) system. Positive and negative values of the variable x and various values of the variable t were taken with the initial conditions of the system as well as the values of the parameters . The efficiency of the method was verified, as the results obtained were compared with the accurate solution of the system. We noticed that the results are very accurate and the effectiveness of the method was confirmed.

Highlights

Drinfeld-Sokolov-Wilson (DSW) system [6, 7, and 19] has many uses in solving nonlinear partial differential equations, as this system provides a set of convergent numerical solutions to its users
Sumudu transform with Adomian decomposition method was used by the researchers (Trushit Patel and Ramakanta Meher) [12] in their research (Adomian Decomposition Sumudu Transform Method for Solving Fully Nonlinear Fractional Order Power-Law Fin-Type Problems), widely acceptable results were obtained, which indicates the possibility of using Sumudu transform with Adomian decomposition method to solve many non-linear problems
Adomian Decomposition Method It can be used and applied in many linear problems and equations in various sciences and mathematical, Adomian decomposition method in its modified form was introduced by Wazwaz [16], this method provides accelerated approximate solutions, and it can be combined with Sumudu transform to solve some problems related to nonlinear partial differential equations

Summary

Introduction

Drinfeld-Sokolov-Wilson (DSW) system [6, 7, and 19] has many uses in solving nonlinear partial differential equations, as this system provides a set of convergent numerical solutions to its users. The Drinfeld-Sokolov-Wilson (DSW) system was solved using several numerical methods including the Homotopy analysis method [1, 11, and 13], the F-expansion method [18], the decomposition method [8], the Tan method [10] and many more methods. We will use the Sumudu transformation with Adomian decomposition method to solve this system in a numerical analysis method. In the first section of this paper, an introduction to the (DSW) system and its uses was presented, as well as an introduction to Sumudu transform with Adomian decomposition method. In the third section it was shown Describe Sumudu Transform with Adomian Decomposition Method to the Coupled Drinfeld – Sokolov – Wilson (DSW) System.

Mathematical model

Numerical results

Conclusion