The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations

2009 ◽  
Vol 22 (4) ◽  
pp. 334-351 ◽  
Author(s):  
Zayed E. M. E. and Abdel Rahman H. M.
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Coupled Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

scholarly journals Solving Fractional-Order Logistic Equation Using a New Iterative Method

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Iterative Method ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Logistic Equation ◽  
Series Solutions ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
New Iterative Method

A fractional version of logistic equation is solved using new iterative method proposed by Daftardar-Gejji and Jafari (2006). Convergence of the series solutions obtained is discussed. The solutions obtained are compared with Adomian decomposition method and homotopy perturbation method.

scholarly journals Solution of Temperature Distribution in a Radiating Fin Using Homotopy Perturbation Method

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
M. J. Hosseini ◽  
M. Gorji ◽  
M. Ghanbarpour
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Analytic Approximation ◽  
Enhance Heat Transfer ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Extended Surfaces ◽  
Comparison Of The Results

Radiating extended surfaces are widely used to enhance heat transfer between primary surface and the environment. The present paper applies the homotopy perturbation to obtain analytic approximation of distribution of temperature in heat fin radiating, which is compared with the results obtained by Adomian decomposition method (ADM). Comparison of the results obtained by the method reveals that homotopy perturbation method (HPM) is more effective and easy to use.

scholarly journals Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hossein Jafari ◽  
Khadijeh Bagherian ◽  
Seithuti P. Moshokoa
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Type Problem ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. We solve the fractional Bratu-type problem as an illustrative example.

scholarly journals An Approached Solution of Wave Equation with Cubic Damping by Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian Decomposition Method (ADM)

2018 ◽  
Vol 10 (2) ◽  
pp. 166
Author(s):  
Moussa BAGAYOGO ◽  
Youssouf PARE ◽  
Youssouf MINOUNGOU
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
The Given

In this study, we consider the wave equation with cubic damping with its initial conditions. Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian decomposition Method (ADM) are applied to this equation. Then, the solution yielding the given initial conditions is gained. Finally, the solutions obtained by each method are compared.

Based on the Improved Homotopy Perturbation Method for Solving Nonlinear Equations

2013 ◽  
Vol 275-277 ◽  
pp. 836-840
Author(s):  
Xi Qin He ◽  
Hai Yang Li
Keyword(s):  
Integral Equation ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

According to Nonlinear Fredholm differential and integral equation，it is proposed that the improved homotopy perturbation method is used to solve in this paper, and apply the numerical examples to compare the advantages among homotopy perturbation method, Adomian decomposition method and improved homotopy perturbation method . The results show that improved homotopy perturbation method is more effective.

scholarly journals Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Abdoul R. Ghotbi ◽  
A. Barari ◽  
D. D. Ganji
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Predator Prey ◽  
Homotopy Perturbation ◽  
Prey System ◽  
Adomian Decomposition ◽  
Wide Range ◽  
Ratio Dependent

Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.

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