Solving nonlinear partial differential equations using the modified variational iteration Padé technique

In this paper, the modified variational iteration method (MVIM) is reintroduced with the enhancement of Pade approximants to lengthen the interval of convergence of VIM or MVIM when used alone in solving nonlinear problems. KdV, mKdV, Burger's and Lax's equations are used as examples to illustrate the effectiveness and convenience of the proposed technique.

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

[2]  C. S. Gardner,et al.  Korteweg‐de Vries Equation and Generalizations. III. Derivation of the Korteweg‐de Vries Equation and Burgers Equation , 1969 .

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

[4]  G. A. Baker.  Essentials of Padé approximants , 1975 .

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

[6]  Magdy A. El-Tawil,et al.  The Solution of KdV and mKdV Equations Using Adomian Pade Approximation , 2004 .

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

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

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

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

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

[12]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[13]  Ji-Huan He.  Homotopy Perturbation Method for Bifurcation of Nonlinear Problems , 2005 .

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

[15]  Tamer A. Abassy,et al.  The solution of Burgers’ and good Boussinesq equations using ADM–Padé technique , 2007 .

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

[17]  Ahmed A. Bahnasawi,et al.  Solving Riccati differential equation using Adomian's decomposition method , 2004, Appl. Math. Comput..