Numerical solution of non‐linear Klein–Gordon equations by variational iteration method

In this paper, numerical solution of non-linear Klein–Gordon equations with power law non-linearities are obtained by the new application of He's variational iteration method. Numerical illustrations that include non-linear Klein–Gordon equations and non-linear partial differential equations are investigated to show the pertinent features of the technique. Copyright © 2006 John Wiley & Sons, Ltd.

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

[2]  M. Ortiz,et al.  A variational r‐adaption and shape‐optimization method for finite‐deformation elasticity , 2004 .

[3]  A. Wazwaz.  A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems , 2001 .

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

[5]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[6]  Jörn Mosler,et al.  On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations , 2006, International Journal for Numerical Methods in Engineering.

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

[8]  Sirendaoreji.  Auxiliary equation method and new solutions of Klein-Gordon equations , 2007 .

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

[10]  Abdul-Majid Wazwaz,et al.  Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations , 2006 .

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

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

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

[14]  Abdul-Majid Wazwaz,et al.  The modified decomposition method for analytic treatment of differential equations , 2006, Appl. Math. Comput..

[15]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[16]  Ji-Huan He.  Approximate solution of nonlinear differential equations with convolution product nonlinearities , 1998 .

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