Application of optimal homotopy asymptotic method for Lane-Emden and Emden-Fowler initial and boundary value problems

2019 ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Shafiq Ullah
Keyword(s):  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Boundary Value ◽  
Optimal Homotopy Asymptotic Method

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 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.

scholarly journals Numerical Scheme for Solving Singular Two-Point Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
N. Ratib Anakira ◽  
A. K. Alomari ◽  
I. Hashim
Keyword(s):  
Exact Solution ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Numerical Scheme ◽  
Boundary Value ◽  
Point Boundary ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Optimal Homotopy Asymptotic Method ◽  
A New Technique

Singular two-point boundary value problems (BVPs) are investigated using a new technique, namely, optimal homotopy asymptotic method (OHAM). OHAM provides a convenient way of controlling the convergence region and it does not need to identify an auxiliary parameter. The effectiveness of the method is investigated by comparing the results obtained with the exact solution, which proves the reliability of the method.

scholarly journals An Algorithm: Optimal Homotopy Asymptotic Method for Solutions of Systems of Second-Order Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Rafiq Mufti ◽  
Muhammad Imran Qureshi ◽  
Salem Alkhalaf ◽  
S. Iqbal
Keyword(s):  
Exact Solutions ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Small Perturbations ◽  
Forcing Function ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear And Nonlinear Systems

Optimal homotopy asymptotic method (OHAM) is proposed to solve linear and nonlinear systems of second-order boundary value problems. OHAM yields exact solutions in just single iteration depending upon the choice of selecting some part of or complete forcing function. Otherwise, it delivers numerical solutions in excellent agreement with exact solutions. Moreover, this procedure does not entail any discretization, linearization, or small perturbations and therefore reduces the computations a lot. Some examples are presented to establish the strength and applicability of this method. The results reveal that the method is very effective, straightforward, and simple to handle systems of boundary value problems.

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.

Sign in / Sign up

Export Citation Format

Share Document