scholarly journals Comments on “Homotopy Perturbation Method for Solving Reaction-Diffusion Equations”

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Afgan Aslanov
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Diffusion Type ◽  
Homotopy Perturbation ◽  
False Conclusion ◽  
Correct Form

The paper entitled“Homotopy perturbation method for solving reaction diffussion equation”contains some mistakes and misinterpretations along with a false conclusion. Applying the homotopy perturbation method (HPM) in an incorrect manner, the authors have drawn the false conclusion that this approach is efficient for reaction-diffusion type of equation. We show that HPM in the proposed form is not efficient in most cases, and hence, we will introduce the correct form of HPM.

scholarly journals Homotopy Perturbation Method for Solving Reaction-Diffusion Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Yu-Xi Wang ◽  
Hua-You Si ◽  
Lu-Feng Mo
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
High Accuracy ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Unknown Parameters ◽  
Weighted Residuals ◽  
Homotopy Perturbation ◽  
Method Of Weighted Residuals

The homotopy perturbation method is applied to solve reaction-diffusion equations. In this method, the trial function (initial solution) is chosen with some unknown parameters, which are identified using the method of weighted residuals. Some examples are given. The obtained results are compared with the exact solutions, revealing that this method is very efficient and the obtained solutions are of high accuracy.

Analytical Solution of Linear and Non-Linear Space-Time Fractional Reaction-Diffusion Equations

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Sefa A Sezer
Keyword(s):  
Analytical Solution ◽  
Linear Space ◽  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Fractional Reaction

In this study, we present the homotopy perturbation method (HPM) for finding the analytical solution of linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. These equations are obtained from standard reaction-diffusion equations by replacing a second-order space deri-vative by a fractional derivative of order and a first-order time derivative by a fractional derivative of order. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to linear and non-linear space-time fractional reaction-diffusion equations.

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