Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations

In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to solve nonlinear oscillator differential equations. Illustrative examples reveal that these methods are very effective and convenient for solving nonlinear differential equations. Moreover, the methods do not require linearization or small perturbation. Comparisons are also made between the exact solutions and the results of the homotopy perturbation method and variational iteration method in order to prove the precision of the results obtained from both methods mentioned.

[1]  Davood Domiri Ganji,et al.  Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method , 2006 .

[2]  Davood Domiri Ganji,et al.  Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations , 2007 .

[3]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[4]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[5]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[6]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[7]  S. H. Behiry,et al.  A new algorithm for the decomposition solution of nonlinear differential equations , 2007, Comput. Math. Appl..

[8]  H. M. Daniali,et al.  The variational iteration method for nonlinear oscillators with discontinuities , 2007 .

[9]  M. M. El-Dessoky,et al.  Synchronization of van der Pol oscillator and Chen chaotic dynamical system , 2008 .

[10]  Shaher Momani,et al.  Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations , 2007, Comput. Math. Appl..

[11]  Ji-Huan He SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[12]  Ji-Huan He A new approach to nonlinear partial differential equations , 1997 .

[13]  Davood Domiri Ganji,et al.  Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM , 2007 .

[14]  Ji-Huan He,et al.  Variational iteration method: New development and applications , 2007, Comput. Math. Appl..

[15]  H. Gottlieb VELOCITY-DEPENDENT CONSERVATIVE NONLINEAR OSCILLATORS WITH EXACT HARMONIC SOLUTIONS , 2000 .

[16]  Ji-Huan He Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[17]  Ji-Huan He Homotopy perturbation technique , 1999 .

[18]  G. Adomian Nonlinear Stochastic Operator Equations , 1986 .

[19]  D Gangi,et al.  APPLICATION OF HES HOMOTOPY-PERTURBATION METHOD TO NONLINEAR COUPLED SYSTEMS OF REACTION-DIFFUSION EQUATIONS , 2006 .