Analytical solutions to heat transfer equations by homotopy-perturbation method revisited

2008 ◽  
Vol 372 (8) ◽  
pp. 1240-1243 ◽  
Author(s):  
M.S.H. Chowdhury ◽  
I. Hashim
Keyword(s):  
Heat Transfer ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Transfer Equations

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

scholarly journals Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations

2017 ◽  
Vol 21 (4) ◽  
pp. 1843-1846 ◽  
Author(s):  
Zhen-Jiang Liu ◽  
Magaji Adamu ◽  
Enoch Suleiman ◽  
Ji-Huan He
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Initial Approximation ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Linear Differential

Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation.

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