The Application of the Homotopy Perturbation Method and theHomotopy Analysis Method to the Generalized Zakharov Equations | Zendy

Hassan A. Zedan | Zendy; Eman El Adrous | Zendy

Open Access

The Application of the Homotopy Perturbation Method and theHomotopy Analysis Method to the Generalized Zakharov Equations

Author(s) -

Hassan A. Zedan,

Eman El Adrous

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/561252

Subject(s) - adomian decomposition method , mathematics , homotopy analysis method , homotopy perturbation method , nonlinear system , computation , homotopy , perturbation (astronomy) , exact solutions in general relativity , mathematical analysis , boundary value problem , partial differential equation , pure mathematics , algorithm , physics , quantum mechanics

We introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented

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