An investigation of nonlinear KdV type equations using HPM and VIM

H  Goodarzian; M  Ghobadi; M A  Farahabadi; H  Mohammadnezhad  and S S  Hejazi

doi:10.17485/ijst/2011/v4i8.26

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An investigation of nonlinear KdV type equations using HPM and VIM

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2011/v4i8.26

Year: 2011, Volume: 4, Issue: 8, Pages: 952-956

Original Article

An investigation of nonlinear KdV type equations using HPM and VIM

H. Goodarzian^1* , M. Ghobadi² , M.A. Farahabadi³ , H. Mohammadnezhad⁴ and S.S. Hejazi¹

¹ Young Researchers Club, Islamic Azad University- Jouybar Branch, Jouybar, Iran
² Sama Technical and Vocational Training College, Islamic Azad University, Sari Branch, Sari, Iran
³ Islamic Azad University- Qaemshahr Branch, Qaemshahr, Iran
⁴ Islamic Azad University- Sari branch, Sari, Iran
¹Young Researchers Club, Islamic Azad University, Jouybar Branch, Jouybar, Iran
[email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The KdV equation appears in fluid mechanics. This equation incorporates both convection and diffusion in fluid dynamics, and is used to describe the structure of shock waves. The objective of this paper is to present a comparative study of He's Homotopy perturbation method (HPM) and variational iteration method (VIM) for the semi analytical solution of three different Kortweg-de Vries (KdV) type equations called KdV, K(2,2,) and modified KdV (Burgers) equations. The study has been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.
Keywords: Variational Iteration Method (VIM); Homotopy Perturbation Method (HPM); KdV Equation; Modified KdV Equation.