Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation

2008 ◽  
Vol 35 (1) ◽  
pp. 93-102 ◽  
Author(s):  
G. Domairry ◽  
N. Nadim
Keyword(s):  
Heat Transfer ◽  
Perturbation Method ◽  
Homotopy Analysis Method ◽  
Transfer Equation ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Equation ◽  
Analysis Method ◽  
Linear Heat ◽  
Homotopy Perturbation ◽  
Homotopy Analysis

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 Assessment of homotopy perturbation method in nonlinear convective-radiative non-Fourier conduction heat transfer equation with variable coefficient

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 263-274 ◽  
Author(s):  
Mohsen Torabi ◽  
Hessameddin Yaghoobi ◽  
Seyfolah Saedodin
Keyword(s):  
Heat Transfer ◽  
Perturbation Method ◽  
Transfer Equation ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Equation ◽  
Conduction Heat Transfer ◽  
Homotopy Perturbation ◽  
Runge Kutta Method ◽  
Engineering Problems ◽  
Specific Heat Coefficient

Analytical solutions play a very important role in heat transfer. In this paper, the He's homotopy perturbation method (HPM) has been applied to nonlinear convective-radiative non-Fourier conduction heat transfer equation with variable specific heat coefficient. The concept of the He's homotopy perturbation method are introduced briefly for applying this method for problem solving. The results of HPM as an analytical solution are then compared with those derived from the established numerical solution obtained by the fourth order Runge-Kutta method in order to verify the accuracy of the proposed method. The results reveal that the HPM is very effective and convenient in predicting the solution of such problems, and it is predicted that HPM can find a wide application in new engineering problems.

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