He’s homotopy perturbation method for systems of integro-differential equations

Abstract In this article, the homotopy perturbation method [He JH. Homotopy perturbation technique. Comput Meth Appl Mech Eng 1999;178:257–62; He JH. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-Linear Mech 2000;35(1):37–43; He JH. Comparison of homotopy perturbation method and homotopy analysis method. Appl Math Comput 2004;156:527–39; He JH. Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 2003;135:73–79; He JH. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 2004;151:287–92; He JH. Application of homotopy perturbation method to nonlinear wave equations Chaos, Solitons & Fractals 2005;26:695–700] is applied to solve linear and nonlinear systems of integro-differential equations. Some nonlinear examples are presented to illustrate the ability of the method for such system. Examples for linear system are so easy that has been ignored.

[1]  A. Zeb,et al.  Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates , 2008 .

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

[3]  D Gangi,et al.  APPLICATION OF HES HOMOTOPY-PERTURBATION METHOD TO NONLINEAR COUPLED SYSTEMS OF REACTION-DIFFUSION EQUATIONS , 2006 .

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

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

[6]  Saeid Abbasbandy,et al.  Application of He’s homotopy perturbation method to functional integral equations , 2007 .

[7]  Abdul Majeed Siddiqui,et al.  Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane , 2008 .

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

[9]  R. Mahmood,et al.  Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder , 2006 .

[10]  Qi Wang.  Homotopy perturbation method for fractional KdV-Burgers equation , 2008 .

[11]  Ahmet Yildirim,et al.  A note on He’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity , 2007 .

[12]  D. Ganji.  The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer , 2006 .

[13]  X.-C. Cai,et al.  Approximate Period Solution for a Kind of Nonlinear Oscillator by He's Perturbation Method , 2006 .

[14]  Livija Cveticanin,et al.  Homotopy–perturbation method for pure nonlinear differential equation , 2006 .

[15]  Davood Domiri Ganji,et al.  Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method , 2006 .

[16]  Ali H. Nayfeh,et al.  Problems in Perturbation , 1985 .

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

[18]  S. Liao.  An approximate solution technique not depending on small parameters: A special example , 1995 .

[19]  T. Hayat,et al.  Homotopy Perturbation Method and Axisymmetric Flow over a Stretching Sheet , 2006 .

[20]  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 .

[21]  Shijun Liao,et al.  Boundary element method for general nonlinear differential operators , 1997 .