scholarly journals Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Muhammad Aslam Noor
Keyword(s):  
Perturbation Method ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.

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 Analyzing “Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problem”

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Afgan Aslanov
Keyword(s):  
Boundary Value Problem ◽  
Perturbation Method ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Efficient Method ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Homotopy Perturbation

We analyze a previous paper by S. T. Mohyud-Din and M. A. Noor (2007) and show the mistakes in it. Then, we demonstrate a more efficient method for solving fourth-order boundary value problems.

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 Numerical Solutions of Fifth and Sixth Order Nonlinear Boundary Value Problems by Daftardar Jafari Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Inayat Ullah ◽  
Hamid Khan ◽  
M. T. Rahim
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Sixth Order ◽  
Nonlinear Boundary Value Problems ◽  
Adomian Decomposition ◽  
Variation Iteration Method

Fifth and sixth order boundary value problems are solved using Daftardar Jafari method (DJM). DJM is introduced by Daftardar-Gejji and Jafari (2006). The approach provides the solution in the form of a rapidly convergent series. The comparison among Daftardar Jafari method (DJM), Adomian decomposition method (ADM), homotopy perturbation method (HPM), variation iteration method (VIM), and the iterative method (ITM) are displayed in table form which shows the efficiency of DJM for the solution of fifth and sixth order BVPs.

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