Solving two-point boundary value problems using combined homotopy perturbation method and Green’s function method

2009 ◽  
Vol 212 (2) ◽  
pp. 366-376 ◽  
Author(s):  
Yong-Gang Wang ◽  
Hui-Fang Song ◽  
Dan Li
Keyword(s):  
Perturbation Method ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Function Method ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Green’S Function Method ◽  
Homotopy Perturbation

scholarly journals Green’s function homotopy perturbation method for the initial-boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Wannika Sawangtong ◽  
Panumart Sawangtong
Keyword(s):  
Perturbation Method ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Initial Boundary Value

Abstract This article deals with the novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method, shortly called SGHPM. The SGHPM is a method which combines the homotopy perturbation method with Green’s function method. The convergence analysis for the SGHPM is shown. Furthermore, some examples are presented to illustrate the validity of the proposed method and to ensure that SGHPM is a technique which is powerful and efficient for finding approximate analytic solutions of IBVPs.

scholarly journals Application of Optimal Homotopy Asymptotic Method to Some Well-Known Linear and Nonlinear Two-Point Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Muhammad Asim Khan ◽  
Shafiq Ullah ◽  
Norhashidah Hj. Mohd Ali
Keyword(s):  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Small Perturbations ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear And Nonlinear ◽  
Semianalytical Method

The objective of this paper is to obtain an approximate solution for some well-known linear and nonlinear two-point boundary value problems. For this purpose, a semianalytical method known as optimal homotopy asymptotic method (OHAM) is used. Moreover, optimal homotopy asymptotic method does not involve any discretization, linearization, or small perturbations and that is why it reduces the computations a lot. OHAM results show the effectiveness and reliability of OHAM for application to two-point boundary value problems. The obtained results are compared to the exact solutions and homotopy perturbation method (HPM).

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.

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