Variational Homotopy Perturbation Method for the Nonlinear Generalized Regularized Long Wave Equation

Amruta Daga^1, and Vikas Pradhan¹

¹Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat, India

Cite this paper

Amruta Daga and Vikas Pradhan. Variational Homotopy Perturbation Method for the Nonlinear Generalized Regularized Long Wave Equation. American Journal of Applied Mathematics and Statistics. 2014; 2(4):231-234. doi: 10.12691/AJAMS-2-4-10

Abstract

This paper presents Variational Homotopy Perturbation method for the nonlinear Generalized Regularized Long Wave (GRLW) equation. The solution of nonlinear GRLW equation is obtained and is solved using the iteration method which is combination of Variational Iteration method and Homotopy Perturbation Method. An example of the propagation of single soliton is given to show the precision of this method.

Keywords

generalized regularized long wave equation, soliton, Variational Homotopy Perturbation method, Variation Iteration Method

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	A.A. Soliman, Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method, Mathematics andComputers in Simulation, 70 (2005) 119-124.
[2]	A.K. Khalifa, K.R. Raslan, H.M. Alzubaidi, Numerical study using ADM for the modified regularized long wave equation, Applied Mathematical Modelling,32 (2008) 2962-2972.
[3]	A.K. Khalifaa, K.R. Raslan, H.M. Alzubaidi, A collocation method with cubic B-splines for solving the MRLWequation, Journal of Computational and Applied Mathematics, 82 (2005) 369-80.
[4]	D. Kaya, A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation, Applied Mathematics and Computation, 149 (2004) 833-841.
[5]	D. Kaya, Salah M.El-Sayed, An application of the decomposition method for the generalized KdV and RLW equations, Chaos, Solitons and Fractals,17 (2003) 869-877.
[6]	D.H. Pregrine, Calculations of the development of an undular bore, J.Fluid Mech, 25 (2003) (1996) 321-330.
[7]	E. Yusufoglu, A. Bekir, Application of the variational iteration method to the regularized long wave equation, Computers and Mathematics with Applications, 25 (2003) (1996) 321-330.
[8]	J. H. He, Variational iteration method kind of non-linear analytical technique:Some examples, Int. J. Non-Linear Mech, 34, pp.699-708, 1999.
[9]	M. A. Noor and S. T. Mohyud-Din, Variational homotopy perturbation method for solving higher dimensional initial boundary value problems,Mathematical Problems in Engineering, Article ID 696734, 2008.
[10]	M. Rafei, D.D. Ganji, H.R. Mohammadi Daniali, H. Pashaei, Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations, Physics Letters A,364 (2007) 1-6.
[11]	Wang Ju-Feng, Bai Fu-Nong and and Cheng Yu-Min, “A meshless method for the nonlinear generalized regularized long wave equation” Chin. Phys. B Vol. 20, No. 3 (2011).
[12]	Yildiray Keskin, “Numerical Solution of Regularized Long Wave Equationby Reduced Differential Transform Method”, Applied Mathematical Sciences, Vol. 4, 2010, no. 25, 1221-1231.