A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations

2009 ◽  
Vol 14 (8) ◽  
pp. 3261-3265 ◽  
Author(s):  
Yahya Qaid Hasan ◽  
Liu Ming Zhu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

scholarly journals A Modified Adomian Decomposition Method for Solving Higher-Order Singular Boundary Value Problems

2010 ◽  
Vol 65 (12) ◽  
pp. 1093-1100 ◽  
Author(s):  
Weonbae Kim ◽  
Changbum Chun
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Adomian Polynomials ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, we present a reliable modification of the Adomian decomposition method for solving higher-order singular boundary value problems. He’s polynomials are also used to overcome the complex and difficult calculation of Adomian polynomials occurring in the application of the Adomian decomposition method. Numerical examples are given to illustrate the accuracy and efficiency of the presented method, revealing its reliability and applicability in handling the problems with singular nature.

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.

scholarly journals A Novel Modification of Adomian Decomposition Method for Singular BVPs of Emden-Fowler Type

2020 ◽  
pp. 84-100 ◽  
Author(s):  
Somaia Ali Alaqel ◽  
Yahya Qaid Hasan
Keyword(s):  
Decomposition Method ◽  
Complete Solution ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Numerical Result ◽  
Adomian Decomposition ◽  
Fowler Equation

In this paper, we apply a novel Modied of Adomian Decomposition Method (MADM) for solving Singular Boundary Value Problems (BVPs) of Emden-Fowler type of higher order. The higher-order Emden-Fowler equation is characterized by two types. In addition, we test the presented method by several linear and nonlinear examples, and compared the numerical result with the exact solution to illustrate performance and reliability of this method in nding approximate solutions as well as its successful in getting the complete solution in many case.

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