Application of homotopy perturbation method to multidimensional partial differential equations

In this paper, an application of homotopy perturbation method (HPM) is applied to solve the kindly of multidimensional partial differential equation such as Helmholtz equation. Comparisons are made between the Adomians decomposition method and HPM. The results reveal that the HPM is very effective and simple and gives the exact solution.

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

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

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

[4]  HeJi-Huan,et al.  Homotopy Perturbation Method , 2003, Advanced Numerical and Semi-Analytical Methods for Differential Equations.

[5]  Hossein Jafari,et al.  Application of Homotopy-Perturbation Method for Solving Gas Dynamics Equation , 2008 .

[6]  Ji-Huan He,et al.  Recent development of the homotopy perturbation method , 2008 .

[7]  J. Miller Numerical Analysis , 1966, Nature.

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

[9]  Nasser Hassan Sweilam,et al.  Homotopy perturbation method for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations , 2008 .

[10]  David J. Evans,et al.  The numerical solution of multidimensional partial differential equations by the decomposition method , 2003, Int. J. Comput. Math..

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

[12]  Davood Domiri Ganji,et al.  Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations , 2007 .

[13]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[14]  Hamid Reza Mohammadi Daniali,et al.  Numerical simulation of the generalized Huxley equation by He's homotopy perturbation method , 2007, Appl. Math. Comput..

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

[16]  Curtis F. Gerald,et al.  APPLIED NUMERICAL ANALYSIS , 1972, The Mathematical Gazette.