AM  Vol.6 No.4 , April 2015
Variational Homotopy Perturbation Method for Solving Benjamin-Bona-Mahony Equation
ABSTRACT
In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Comparison with Adomian’s decomposition method, homotopy perturbation method, and with the exact solution shows that VHPM is more effective and accurate than ADM and HPM, and is reliable and manageable for this type of equation.

Cite this paper
Easif, F. , Manaa, S. , Mahmood, B. and Yousif, M. (2015) Variational Homotopy Perturbation Method for Solving Benjamin-Bona-Mahony Equation. Applied Mathematics, 6, 675-683. doi: 10.4236/am.2015.64062.
References
[1]   Wazwaz, A.M. (2005) Nonlinear Variants of KDV and Application to Thin Film Flow. Central European Journal of Physics, KP Equations with Compactons, Solitons and Periodic, 3, 648-653.

[2]   He, J.H. (1999) Variational Iteration Method—A Kind of Non-Linear Analytical Technique: Some Examples. International Journal of Non-Linear Mechanics, 34, 699-708.
http://dx.doi.org/10.1016/S0020-7462(98)00048-1

[3]   He, J.H. (1999) Homotopy Perturbation Technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262.
http://dx.doi.org/10.1016/S0045-7825(99)00018-3

[4]   Benjamin, T.B. (1974) Lectures on Nonlinear Wave Motion. Lecture Notes in Applied Mathematics, 15, 3-47.

[5]   Benjamin, T.B., Bona, J.L. and Mahony, J.J. (1972) Model Equations for Long Waves in Nonlinear Dispersive System. Philos. Trans. Soc., London S. R., A., 272, 47-78.

[6]   Wu, G.C. (2013) Challenge in the Variational Iteration Method—A New Approach to Identification of the Lagrange Multipliers. Journal of King Saud University, 25, 175-178.
http://dx.doi.org/10.1016/j.jksus.2012.12.002

[7]   He, J.H. (1997) A New Approach to Nonlinear Partial Differential Equations. Communications in Nonlinear Science and Numerical Simulation, 2, 230-235.
http://dx.doi.org/10.1016/S1007-5704(97)90007-1

[8]   He, J.H. (1999) Homotopy Perturbation Technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262.
http://dx.doi.org/10.1016/S0045-7825(99)00018-3

[9]   Muhammad, A.N. and Syed, T.M. (2008) Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems. Mathematical Problems in Engineering, Article ID: 696734, 11 p.

[10]   Hasan, B., Mehmet, H.B., Seyma, T. and Tojga, A. (2011) A Comparison between HPM and ADM for the Nonlinear Benjamin-Bona-Mahony Equation. International Journal of Basic and Applied Science, 11, 117-127.

 
 
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