Variational approach for nonlinear oscillators with discontinuities

In this paper, He's variational approach is applied to the nonlinear oscillators with discontinuities. We conclude that the method is very effective, accurate and convenient. Moreover, the approximate solutions obtained are uniformly valid for both small parameters and large parameters.

[1]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[2]  C. Bender,et al.  A new perturbative approach to nonlinear problems , 1989 .

[3]  Ji-Huan He,et al.  Preliminary report on the energy balance for nonlinear oscillations , 2002 .

[4]  S. Abbasbandy.  A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials , 2007 .

[5]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[6]  Ji-Huan He,et al.  Application of Parameter-expanding Method to Strongly Nonlinear Oscillators , 2007 .

[7]  Hamid Reza Mohammadi Daniali,et al.  Variational iteration method for solving the epidemic model and the prey and predator problem , 2007, Appl. Math. Comput..

[8]  Hamid Reza Mohammadi Daniali,et al.  Solution of the epidemic model by homotopy perturbation method , 2007, Appl. Math. Comput..

[9]  Ahmet Yildirim,et al.  A Comparative Study of He's Homotopy Perturbation Method for Determining Frequency-amplitude Relation of a Nonlinear Oscillator with Discontinuities , 2007 .

[10]  D. Ganji.  The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer , 2006 .

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

[12]  Ji-Huan He,et al.  Determination of limit cycles for strongly nonlinear oscillators. , 2003, Physical review letters.

[13]  Hong-Mei Liu,et al.  Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt–Poincare method , 2005 .

[14]  Ji-Huan He,et al.  Variational principles for some nonlinear partial differential equations with variable coefficients , 2004 .

[15]  Davood Domiri Ganji,et al.  The application of He's variational iteration method to nonlinear equations arising in heat transfer , 2007 .

[16]  Davood Domiri Ganji,et al.  Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations , 2007 .

[17]  Ji-Huan He.  Approximate analytical solution for seepage flow with fractional derivatives in porous media , 1998 .

[18]  Davood Domiri Ganji,et al.  Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method , 2006 .

[19]  Ji-Huan He,et al.  Semi-Inverse Method of Establishing Generalized Variational Principles for Fluid Mechanics With Emphasis on Turbomachinery Aerodynamics , 1997 .

[20]  Ji-Huan He,et al.  Modified Lindstedt–Poincare methods for some strongly non-linear oscillations: Part II: a new transformation , 2002 .

[21]  J.-H. He,et al.  Modified Lindsted-Poincare Methods For Some Strongly Nonlinear Oscillations Part III : Double Series Expansion , 2001 .

[22]  He Ji-huan,et al.  A note on delta-perturbation expansion method , 2002 .

[23]  Ji-Huan He.  Variational approach for nonlinear oscillators , 2007 .

[24]  Augusto Beléndez,et al.  Application of He's Homotopy Perturbation Method to the Duffing-Harmonic Oscillator , 2007 .

[25]  Ji-Huan He,et al.  Α Review on Some New Recently Developed Nonlinear Analytical Techniques , 2000 .

[26]  Ji-Huan He,et al.  The homotopy perturbation method for nonlinear oscillators with discontinuities , 2004, Appl. Math. Comput..

[27]  Ji-Huan He,et al.  Bookkeeping Parameter in Perturbation Methods , 2001 .

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

[29]  Mary L. Boas,et al.  Solving Equations with Physical Understanding , 1985 .

[30]  Lingpeng Yang,et al.  Document reranking by term distribution and maximal marginal relevance for chinese information retrieval , 2007, Information Processing & Management.

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

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

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

[34]  Ji-Huan He,et al.  Modified Lindstedt–Poincare methods for some strongly non-linear oscillations: Part I: expansion of a constant , 2002 .