the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method

Abstract

The aim of this article is to propose an efficient hybrid transform iteration method that combines the homotopy perturbation approach, the variational iteration method, and the Aboodh transform forsolving various partial differential equations. The Korteweg-de Vries (KdV), modified KdV, coupled KdV, and coupled pseudo-parabolic equations are given as examples to show how effective and practical the suggested method is. The obtained exact solitary solutions of the KdV equations as well as the exact solution of the coupled pseudo-parabolic equations are identified as a convergent series with easily calculable components. identified as a convergent series with easily calculable components.

When used to solve KdV , Wave like and  Pseudo – Parabolic equations , the proposed method helps to avoid Problems that frequently arise when determining the Lagrange Multiplier and the difficult integration usedin the variation iteration method , as well as the need to use the transform convolution theorem.