scholarly journals The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey-Stewartson Equations and Comparison between Them and Exact Solutions

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Hassan A. Zedan ◽  
W. Barakati ◽  
Nada Hamad
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Problems ◽  
The Other ◽  
Analysis Method ◽  
Analytic Tool ◽  
Homotopy Perturbation ◽  
Homotopy Analysis

We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained.

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

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Hassan A. Zedan ◽  
Eman El Adrous
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Problems ◽  
Analysis Method ◽  
Homotopy Perturbation ◽  
Homotopy Analysis ◽  
The Absolute

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.

scholarly journals Solution of the Davey–Stewardson equation using homotopuy analysis method

2010 ◽  
Vol 15 (4) ◽  
pp. 423-433 ◽  
Author(s):  
H. Jafari ◽  
M. Alipour
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Analysis Method ◽  
Nls Equation ◽  
Homotopy Perturbation ◽  
Higher Dimensional ◽  
Homotopy Analysis ◽  
Good Agreement

In this paper, the homotopy analysis method (HAM) proposed by Liao is adopted for solving Davey–Stewartson (DS) equations which arise as higher dimensional generalizations of the nonlinear Schrödinger (NLS) equation. The results obtained by HAM have been compared with the exact solutions and homotopy perturbation method (HPM) to show the accuracy of the method. Comparisons indicate that there is a very good agreement between the HAM solutions and the exact solutions in terms of accuracy.

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