HOMOTOPY PERTURBATION AND ADOMIAN DECOMPOSITION METHODS ON 12th-ORDER BOUNDARY VALUE PROBLEMS

2020 ◽  
Vol 9 (12) ◽  
pp. 10671-10682
Author(s):  
E. U. Agom ◽  
F. O. Ogunfiditimi ◽  
E. V. Bassey
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Decomposition Methods ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

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 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 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).

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