He's homotopy perturbation method for nonlinear differential-difference equations

A new scheme, deduced from He's homotopy perturbation method (HPM), is presented for solving nonlinear differential-difference equations (DDEs). A simple but typical example is applied to illustrate the validity and great potential of the generalized HPM in solving nonlinear DDE. The results reveal that the method is very effective and simple.

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

[2]  Reza Mokhtari,et al.  Variational Iteration Method for Solving Nonlinear Differential- Difference Equations , 2008 .

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

[4]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[5]  Ji-Huan He New interpretation of homotopy perturbation method , 2006 .

[6]  Mehdi Dehghan,et al.  Inverse problem of diffusion equation by He's homotopy perturbation method , 2007 .

[7]  Yongtang Wu,et al.  Application of the Hirota bilinear formalism to a new integrable differential-difference equation , 1998 .

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

[9]  Ji-Huan He,et al.  Generalized solitary solution and compacton-like solution of the Jaulent–Miodek equations using the Exp-function method , 2008 .

[10]  Mehdi Dehghan,et al.  SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS USING HE'S HOMOTOPY PERTURBATION METHOD , 2008 .

[11]  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 .

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

[13]  Mehdi Dehghan,et al.  Solution of delay differential equations via a homotopy perturbation method , 2008, Math. Comput. Model..

[14]  Shu-fang Deng,et al.  The Bäcklund transformation and novel solutions for the Toda lattice , 2005 .

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

[16]  M. Ablowitz,et al.  On the solution of a class of nonlinear partial di erence equations , 1977 .

[17]  Ahmet Yildirim,et al.  Traveling Wave Solution of Korteweg-de Vries Equation using He's Homotopy Perturbation Method , 2007 .

[18]  S D Zhu,et al.  Exp-function Method for the Discrete mKdV Lattice , 2007 .

[19]  E. Yusufoglu,et al.  Homotopy Perturbation Method for Solving a Nonlinear System of Second Order Boundary Value Problems , 2007 .

[20]  Manuel Mañas,et al.  Darboux transformations for multidimensional quadrilateral lattices. I , 1997 .

[21]  Mehdi Dehghan,et al.  Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method , 2007 .

[22]  M. Dehghan,et al.  Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems , 2009 .

[23]  Changbum Chun,et al.  Solitons and periodic solutions for the fifth-order KdV equation with the Exp-function method , 2008 .

[24]  Elçin Yusufoglu,et al.  An efficient algorithm for solving integro-differential equations system , 2007, Appl. Math. Comput..

[25]  Lei Wu,et al.  Adomian decomposition method for nonlinear differential-difference equations , 2009 .

[26]  Ji-Huan He,et al.  Comparison of homotopy perturbation method and homotopy analysis method , 2004, Appl. Math. Comput..

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

[28]  S D Zhu,et al.  Exp-function Method for the Hybrid-Lattice System , 2007 .