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An Investigation of Nonlinear KdV Type Equations Using HPM and VIM


Affiliations
1 Young Researchers Club, Islamic Azad University- Jouybar Branch, Jouybar, Iran, Islamic Republic of
2 Sama Technical and Vocational Training College, Islamic Azad University, Sari Branch, Sari, Iran, Islamic Republic of
3 Islamic Azad University- Qaemshahr Branch, Qaemshahr, India
4 Islamic Azad University- Sari branch, Sari, Iran, Islamic Republic of
5 Young Researchers Club, Islamic Azad University, Jouybar Branch, Jouybar, Iran, Islamic Republic of
 

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

Keywords

Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), KdV Equation, Modified KdV Equation
User

  • Abdou MA and Soliman MA (2005) Variational iteration method for solving Burger's and coupled Burger's equation. J. Comput. Appl. Math. 181, 245- 251.

  • Aboulvafa EM Abdou MA and Mahmoud AA (2006) The solution of nonlinear coagulation problem with mass loss. Chaos Solitons & Fractals. 29, 313-330.

  • Gardner CS Green JM Kruskal MD and Miura RM (1967) Method for solving the Korteweg-deVries equation. Phys. Rev. Lett. 19, 1095–1097.

  • Ganji DD (2006) The application of homotopy perturbation method to nonlinear equations arising in heat transfer. Phys. Lett. A. 355, 337-341.

  • He JH (2005) Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Non-linear Sci. Num. Sim. 6(2), 207-208.

  • He JH (2006a) Homotopy perturbation method for solving boundary value problems. Phys. Lett. A. 350, 87-88.

  • He JH (2006b) Variational approach for nonlinear oscillators. Int. J. Mod. Phys. B . 20, 1141-1199.

  • Korteweg DJ and Vries G (1895) On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave. Philos. Mag. 39, 422–443.

  • Khattak AJ and ul-Islam S (2008) A comparative study of numerical solutions of a class of KdV equation. J. Comput. Appl. Math.199, 425–434.

  • Ozis T and Ozer S (2006) A simple similaritytransformation- iterative scheme applied to Kortewegde Vries equation. Appl. Math. Comput. 173, 19–32.

  • Soliman AA (2006) The modified extended tanhfunction method for solving Burgers-type equations. Physica A. 361, 394–404.

  • Tolou N Khatami I Jafari B and Ganji DD (2008) Analytical Solution of Nonlinear Vibrating Systems. Am. J. Appl. Sci. 5(9), 1219-1224.

  • Wadati M Sanuki H and Konno K (1975) Relationships among inverse method, backlund transformation and an infinite number of conservation laws. Prog. Theoret. Phys. 53, 419–436.

  • Yan ZY and Zhang HQ (2000) Auto-Darboux Transformation and exact solutions of the Brusselator reaction diffusion model. Appl. Math. Mech. 22, 541– 546.

  • Yan ZY and Zhang HQ (2001) New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water. Phys. Lett. A. 285, 355–362.

  • Yan ZY (2001) New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations. Phys. Lett. A. 292, 100–106.

  • Zahedi SA and.Okazi M (2010) An Investigation on two-dimensional non-linear wave equation using VIM. Indian J. Sci. Technol. 3(9), 1006-1008.


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  • An Investigation of Nonlinear KdV Type Equations Using HPM and VIM

Abstract Views: 460  |  PDF Views: 77

Authors

H. Goodarzian
Young Researchers Club, Islamic Azad University- Jouybar Branch, Jouybar, Iran, Islamic Republic of
M. Ghobadi
Sama Technical and Vocational Training College, Islamic Azad University, Sari Branch, Sari, Iran, Islamic Republic of
M. A. Farahabadi
Islamic Azad University- Qaemshahr Branch, Qaemshahr, India
H. Mohammadnezhad
Islamic Azad University- Sari branch, Sari, Iran, Islamic Republic of
S. S. Hejazi
Young Researchers Club, Islamic Azad University, Jouybar Branch, Jouybar, Iran, Islamic Republic of

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

Keywords


Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), KdV Equation, Modified KdV Equation

References





DOI: https://doi.org/10.17485/ijst%2F2011%2Fv4i8%2F30902