scholarly journals The Optimal Homotopy Asymptotic Method for the Solution of Higher-Order Boundary Value Problems in Finite Domains

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Javed Ali ◽  
S. Islam ◽  
Hamid Khan ◽  
Syed Inayat Ali Shah
Keyword(s):  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Higher Order ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Optimal Homotopy Asymptotic Method ◽  
Finite Domains

We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM). The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM), variational iteration (VIM), homotopy perturbation (HPM), and variational iteration decomposition method (VIDM). The results show that the proposed method is more effective and reliable.

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 Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Fifth Order ◽  
Adomian’S Polynomials

We apply the variational iteration method using He's polynomials (VIMHP) for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007). The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

scholarly journals Solving Singular Boundary Value Problems by Optimal Homotopy Asymptotic Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
S. Zuhra ◽  
S. Islam ◽  
M. Idrees ◽  
Rashid Nawaz ◽  
I. A. Shah ◽  
...  
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Boundary Value ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Optimal Homotopy Asymptotic Method

In this paper, optimal homotopy asymptotic method (OHAM) for the semianalytic solutions of nonlinear singular two-point boundary value problems has been applied to several problems. The solutions obtained by OHAM have been compared with the solutions of another method named as modified adomain decomposition (MADM). For testing the success of OHAM, both of the techniques have been analyzed against the exact solutions in all problems. It is proved by this paper that solutions of OHAM converge rapidly to the exact solution and show most effectiveness as compared to MADM.

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