A new modification of the homotopy perturbation method for linear and nonlinear operators

In this paper we present an efficient modification of the homotopy perturbation method that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy perturbation method. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work. The new modification introduces a promising tool for many linear and nonlinear problems.

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

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

[3]  Abdul-Majid Wazwaz,et al.  A new modification of the Adomian decomposition method for linear and nonlinear operators , 2001, Appl. Math. Comput..

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[20]  Abdul-Majid Wazwaz,et al.  The modified decomposition method for analytic treatment of differential equations , 2006, Appl. Math. Comput..