Approximate and exact solution of Korteweg de Vries problem using Aboodh Adomian polynomial method

Abstract

This study introduce Aboodh Adomian polynomial Method (AAPM) to solve nonlinear third order KdV problems providing it approximate and exact solution. To get the approximate analytical answers to the issues, the Aboodh transform approach was used. Given that the Aboodh transform cannot handle the nonlinear elements in the equation, the Adomian polynomial was thought to be a crucial tool for linearizing the associated nonlinearities. All of the issues examined demonstrated the strength and effectiveness of the Adomian polynomial and Aboodh transforms in solving various nonlinear equations when compared to other well-known methods. To show how this strategy may be applied and is beneficial, three cases were examined.