A reliable treatment of homotopy perturbation method for Klein–Gordon equations

Abstract In this Letter, we present a reliable algorithm of the homotopy perturbation method to the nonlinear Klein–Gordon equations. The algorithm provides analytical approximations for different types of the Klein–Gordon equations. The proposed framework overcomes the difficulty that arising in calculating complicated integrals using the homotopy perturbation method. Some numerical illustrations are given to show the efficiency of the algorithm.

[1]  M. El-shahed.  Application of He's Homotopy Perturbation Method to Volterra's Integro-differential Equation , 2005 .

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

[3]  Ji-Huan He,et al.  Asymptotology by homotopy perturbation method , 2004, Appl. Math. Comput..

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

[5]  R. Mahmood,et al.  Thin Film Flow of a Third Grade Fluid on a Moving Belt by He's Homotopy Perturbation Method , 2006 .

[6]  John D. Gibbon,et al.  The sine-Gordon equation as a model classical field theory , 1975 .

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

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

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

[10]  Ji-Huan He.  Limit cycle and bifurcation of nonlinear problems , 2005 .

[11]  Saeid Abbasbandy,et al.  Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method , 2006, Appl. Math. Comput..

[12]  A. Siddiqui,et al.  Couette and Poiseuille Flows for Non-Newtonian Fluids , 2006 .

[13]  S. Momani,et al.  Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order , 2008 .

[14]  Saeid Abbasbandy,et al.  Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method , 2006, Appl. Math. Comput..

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

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

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

[18]  J. Gibbon,et al.  Solitons and Nonlinear Wave Equations , 1982 .

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

[20]  Salah M. El-Sayed,et al.  A numerical solution of the Klein-Gordon equation and convergence of the decomposition method , 2004, Appl. Math. Comput..

[21]  Ji-Huan He.  Periodic solutions and bifurcations of delay-differential equations , 2005 .