scholarly journals Approximate analytical solutions of reaction–diffusion equations with exponential source term: Homotopy perturbation method (HPM)

2011 ◽  
Vol 24 (10) ◽  
pp. 1634-1639 ◽  
Author(s):  
S.O. Ajadi ◽  
M. Zuilino
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Source Term ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions

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.

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.

scholarly journals Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Accelerated Convergence ◽  
Homotopy Perturbation ◽  
Long Wave ◽  
Approximate Analytical Solutions ◽  
Regularized Long Wave Equation ◽  
Regular Homotopy

The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.

scholarly journals Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xiang Hong ◽  
Jun Wang ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Second Order ◽  
Packaging System ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions

The homotopy perturbation method (HPM) with an auxiliary term was applied to obtain approximate analytical solutions of polymer cushioning packaging system. The second-order solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this modified HPM with convenient calculation.

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