Application of adomian decomposition method for singularly perturbed fourth order boundary value problems

2016 ◽  
Author(s):  
Sinan Deniz ◽  
Necdet Bildik
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Singularly Perturbed ◽  
Adomian Decomposition

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.

A Reliable Treatment for Solving Nonlinear Two-Point Boundary Value Problems

2007 ◽  
Vol 62 (9) ◽  
pp. 483-489
Author(s):  
Mustafa Inc
Keyword(s):  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Shooting Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Adomian Decomposition

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shooting method applied to the solutions of nonlinear two-point BVPs. The comparison shows that the MDM is reliable, efficient and easy for solving the nonlinear twopoint BVPs.

scholarly journals Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Randhir Singh ◽  
Jitendra Kumar ◽  
Gnaneshwar Nelakanti
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Recursive Scheme ◽  
Adomian Decomposition ◽  
Uniqueness Of The Solution ◽  
Transcendental Equations

We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.

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