Numerical solution of sine-Gordon equation by variational iteration method

In this Letter, variational iteration method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

[1]  Ji-Huan He,et al.  An iteration formulation for normalized diode characteristics , 2004, Int. J. Circuit Theory Appl..

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

[3]  S. Momani,et al.  Analytical approach to linear fractional partial differential equations arising in fluid mechanics , 2006 .

[4]  Mark J. Ablowitz,et al.  NUMERICAL HOMOCLINIC INSTABILITIES IN The SINE-GORDON EQUATION , 1992 .

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

[6]  Santanu Saha Ray,et al.  A numerical solution of the coupled sine-Gordon equation using the modified decomposition method , 2006, Appl. Math. Comput..

[7]  M. Wadati,et al.  The Exact Solution of the Modified Korteweg-de Vries Equation , 1972 .

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

[9]  Ji-Huan He Approximate analytical solution of Blasius' equation , 1998 .

[10]  Necdet Bildik,et al.  The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations , 2006 .

[11]  Mark J. Ablowitz,et al.  On the Numerical Solution of the Sine-Gordon Equation , 1996 .

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

[13]  S. Momani,et al.  Numerical methods for nonlinear partial differential equations of fractional order , 2008 .

[14]  X. Y. Wang,et al.  Exact and explicit solitary wave solutions for the generalised fisher equation , 1988 .

[15]  A. Wazwaz The tanh method and a variable separated ODE method for solving double sine-Gordon equation , 2006 .

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

[17]  Dogan Kaya,et al.  An application of the modified decomposition method for two dimensional sine-Gordon equation , 2004, Appl. Math. Comput..

[18]  A. A. Soliman,et al.  A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations , 2006 .

[19]  Abdul-Majid Wazwaz,et al.  Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations , 2006 .

[20]  Tamer A. Abassy,et al.  Toward a modified variational iteration method , 2007 .

[21]  M. A. Abdou,et al.  The solution of nonlinear coagulation problem with mass loss , 2006 .

[22]  Abdul-Majid Wazwaz,et al.  The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations , 2005, Appl. Math. Comput..

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

[24]  A. Jeffrey,et al.  Exact solutions to the KdV-Burgers' equation , 1991 .

[25]  Ishak Hashim,et al.  Numerical simulation of the generalized Huxley equation by He's variational iteration method , 2007, Appl. Math. Comput..

[26]  A. Wazwaz The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations , 2007 .

[27]  A. Wazwaz A comparison between the variational iteration method and Adomian decomposition method , 2007 .

[28]  Dogan Kaya A numerical solution of the sine-Gordon equation using the modified decomposition method , 2003, Appl. Math. Comput..

[29]  Junfeng Lu,et al.  Variational iteration method for solving two-point boundary value problems , 2007 .

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

[31]  Mark J. Ablowitz,et al.  Regular ArticleOn the Numerical Solution of the Sine–Gordon Equation: I. Integrable Discretizations and Homoclinic Manifolds , 1996 .