Application of He's methods to nonlinear chemistry problems

In this paper, He's variational iteration method (VIM) and homotopy perturbation method (HPM) are implemented for solving analytically two systems of ordinary differential equations that often appear in chemical applications. In both methods, the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The solution procedure is of utter simplicity, and the obtained solution is of high accuracy.

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

[2]  M. A. Abdou,et al.  The solution of nonlinear coagulation problem with mass loss , 2006 .

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

[4]  W. Gautschi.  Numerical analysis: an introduction , 1997 .

[5]  Ji-Huan He.  Approximate solution of nonlinear differential equations with convolution product nonlinearities , 1998 .

[6]  Mehdi Dehghan,et al.  Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method , 2008 .

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

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

[9]  Shaher Momani,et al.  Numerical approach to differential equations of fractional order , 2007 .

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

[11]  Davood Domiri Ganji,et al.  ASSESSMENT OF HOMOTOPY-PERTURBATION AND PERTURBATION METHODS IN HEAT RADIATION EQUATIONS , 2006 .

[12]  Dogan Kaya,et al.  A reliable method for the numerical solution of the kinetics problems , 2004, Appl. Math. Comput..

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

[14]  Davood Domiri Ganji,et al.  Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method , 2006 .

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

[16]  A. Wazwaz.  The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations , 2007 .

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

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

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

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

[21]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[22]  H. Weitzner,et al.  Perturbation Methods in Applied Mathematics , 1969 .

[23]  A. A. Soliman,et al.  A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations , 2006 .

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

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

[26]  T. E. Hull,et al.  Comparing Numerical Methods for Ordinary Differential Equations , 1972 .

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

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

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

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

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

[32]  R. Bellman.  Perturbation techniques in mathematics, physics, and engineering , 1972 .

[33]  Shaher Momani,et al.  Application of He’s variational iteration method to Helmholtz equation , 2006 .