He's variational approach for nonlinear oscillators with high nonlinearity

In this paper, He's variational approach is applied to the strongly nonlinear oscillators with high nonlinearity. Some examples are given to illustrate the effectiveness and convenience of this method. Comparison with the exact solutions is also made, revealing that the present method leads to accurate solutions.

[1]  Ji-Huan He Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[2]  Mario D’Acunto,et al.  Self-excited systems: Analytical determination of limit cycles , 2006 .

[3]  Ji-Huan He,et al.  Construction of solitary solution and compacton-like solution by variational iteration method , 2006 .

[4]  Mario D’Acunto,et al.  Determination of limit cycles for a modified van der Pol oscillator , 2006 .

[5]  S. Gallego,et al.  Application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire , 2007 .

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

[7]  T. Hayat,et al.  Homotopy Perturbation Method and Axisymmetric Flow over a Stretching Sheet , 2006 .

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

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

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

[11]  X.-C. Cai,et al.  Approximate Period Solution for a Kind of Nonlinear Oscillator by He's Perturbation Method , 2006 .

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

[13]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[14]  Ji-Huan He Erratum: Determination of Limit Cycles for Strongly Nonlinear Oscillators [ Phys. Rev. Lett. 90, 174301 (2003)] , 2003 .

[15]  Ji-Huan He HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .

[16]  Ji-Huan He Variational iteration method—Some recent results and new interpretations , 2007 .

[17]  A. A. Soliman,et al.  New applications of variational iteration method , 2005 .

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

[19]  Shaher Momani,et al.  Application of He’s variational iteration method to Helmholtz equation , 2006 .

[20]  Baisheng Wu,et al.  Approximate analytical solutions for oscillation of a mass attached to a stretched elastic wire , 2007 .

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

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

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

[24]  J. Liu,et al.  A new method based on the harmonic balance method for nonlinear oscillators , 2007 .

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

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