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Recent Modifications of Adomian Decomposition Method for Initial Value Problem in Ordinary Differential Equations  [PDF]
M. Almazmumy, F. A. Hendi, H. O. Bakodah, H. Alzumi
American Journal of Computational Mathematics (AJCM) , 2012, DOI: 10.4236/ajcm.2012.23030
Abstract: In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are applied to the problem. The effectiveness of the each modified is verified by several examples.
Adomian Decomposition Method for Solving Abelian Differential Equations  [PDF]
Omar K. Jaradat
Journal of Applied Sciences , 2008,
Abstract: In this study, we implement a relatively new analytical technique, the Adomian Decomposition Method (ADM), for solving Abelian differential equations. The analytical and numerical results of the equations have been obtained in terms of convergent series with easily computable components. The method is applied to solve two problems. The current results are compared with these derived from the established Runge-Kutta method in order to verify the accuracy of the ADM. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the ADM is powerful and efficient tool for solving Abelian differential equations.
Restarted Adomian decomposition method for solving Duffing-van der Pol equation
A. R. Vahidi,Z. Azimzadeh,S. Mohammadifar
Applied Mathematical Sciences , 2012,
Abstract:
On Adomian's Decomposition Method for Solving Differential Equations  [PDF]
Petre Dita,Nicolae Grama
Physics , 1997,
Abstract: We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to take correctly into account the behaviour of the solutions in the neighborhood of the singular points.
Adomian Decomposition Method for Solving Goursat's Problems  [PDF]
Mariam A. Al-Mazmumy
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.28134
Abstract: In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached conditions are given on the characteristics curves are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.
Laplace Discrete Adomian Decomposition Method for Solving Nonlinear Integro Differential Equations  [PDF]
H. O. Bakodah, M. Al-Mazmumy, S. O. Almuhalbedi, Lazim Abdullah
Journal of Applied Mathematics and Physics (JAMP) , 2019, DOI: 10.4236/jamp.2019.76093
Abstract:
This paper proposes the Laplace Discrete Adomian Decomposition Method and its application for solving nonlinear integro-differential equations. This method is based upon the Laplace Adomian decomposition method coupled with some quadrature rules of numerical integration. Four numerical examples of integro-differential equations in both Volterra and Fredholm integrals are used to be solved by the proposed method. The performance of the proposed method is verified through absolute error measures between the approximated solutions and exact solutions. The series of experimental numerical results show that our proposed method performs in high accuracy and efficiency. The study clearly highlights that the proposed method could be used to overcome the analytical approaches in solving nonlinear integro-differential equations.
The use of Adomian decomposition method for solving problems in calculus of variations  [PDF]
Mehdi Dehghan,Mehdi Tatari
Mathematical Problems in Engineering , 2006, DOI: 10.1155/mpe/2006/65379
Abstract: In this paper, a numerical method is presented for finding the solution of some variational problems. The main objective is to find the solution of an ordinary differential equation which arises from the variational problem. This work is done using Adomian decomposition method which is a powerful tool for solving large amount of problems. In this approach, the solution is found in the form of a convergent power series with easily computed components. To show the efficiency of the method, numerical results are presented.
Application of the Adomian decomposition method for solving the heat equation in the cast-mould heterogeneous domain  [PDF]
R. Grzymkowski,M. Pleszczyński,D. S?ota
Archives of Foundry Engineering , 2009,
Abstract: The paper is focused on a method for solving the heat equation in a cast-mould heterogeneous domain. The discussed method makes use of the Adomian decomposition method. The derived calculations prove the effectiveness of the method for solving such types of problems.
Adomian decomposition method for solving nonlinear heat equation with exponential nonlinearity  [PDF]
R. Jebari,I. Ghanmi,A. Boukricha
International Journal of Mathematical Analysis , 2013,
Abstract: In this paper, the adomian decomposition method is applied to nonlinearheat equation with exponential nonlinearity. This method istested for some examples. The results obtained show that the methodis efficient and accurate. This study showed also, the speed of the convergentof Adomian decomposition method.
Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems  [PDF]
Waleed Al-Hayani
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.510136
Abstract:

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

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