The Variational Homotopy Perturbation Method for Solving((n×n)+1)Dimensional Burgers’ Equations

F A Hendi,B S Kashkari,A A Alderremy

doi:10.1155/2016/4146323

F A Hendi, B S Kashkari + Show 1 more

Open Access

https://doi.org/10.1155/2016/4146323

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Abstract

The variational homotopy perturbation method VHPM is used for solvingn-dimensional Burgers’ system. Some examples are examined to validate that the method reduced the calculation size, treating the difficulty of nonlinear term and the accuracy.

Highlights

IntroductionThe variational iteration method VIM and the homotopy perturbation method HPM were proposed by He in [1,2,3,4,5,6]
The variational iteration method VIM and the homotopy perturbation method HPM were proposed by He in [1,2,3,4,5,6]. Many researchers used these methods in a variety of scientific fields of partial differential equations PDEs including Burgers’ equation which arises in many of physically important phenomena [7,8,9]
It was shown that the methods are stronger than other techniques such as the Adomian decomposition method [10,11,12,13,14,15,16,17,18]

Summary

Introduction

The variational iteration method VIM and the homotopy perturbation method HPM were proposed by He in [1,2,3,4,5,6]. Many researchers used these methods in a variety of scientific fields of partial differential equations PDEs including Burgers’ equation which arises in many of physically important phenomena [7,8,9]. In our work n-dimensional Burgers’ equation is solved by the variational homotopy perturbation method VHPM which is combination of VIM and HPM.

Variational Iteration Method

Homotopy Perturbation Method

Variational Homotopy Perturbation Method

Application

Conclusion