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.

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.

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.

scholarly journals Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Nonlinear Boundary Value Problems ◽  
Pseudospectral Methods ◽  
New Approach ◽  
Homotopy Perturbation ◽  
Chebyshev Pseudospectral

We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the MHD Jeffery-Hamel flow and the effect of MHD on the flow has been discussed. Comparisons are made between the proposed technique, the previous studies, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the presented approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method at small orders. The MATLAB software has been used to solve all the equations in this study.

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