scholarly journals Using Adomian decomposition method for solving systems of second order ordinary differential equations

2021 ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Second Order ◽  
Adomian Decomposition

scholarly journals Adomian decomposition method for solving initial value problems in vibration models

2018 ◽  
Vol 159 ◽  
pp. 02007
Author(s):  
Sudi Mungkasi ◽  
I Made Wicaksana Ekaputra
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
External Source ◽  
Accurate Solution ◽  
Second Order ◽  
Initial Value ◽  
Adomian Decomposition

A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problems correctly is required in order to get an accurate solution. In this work, we use Adomian decomposition method to solve vibration models in the forms of initial value problems of second-order ordinary differential equations. However, for problems involving an external source, the Adomian decomposition method may not lead to an accurate solution if the external source is not correctly treated. In this paper, we propose a strategy to treat the external source when we implement the Adomian decomposition method to solve initial value problems of second-order ordinary differential equations. Computational results show that our strategy is indeed effective. We obtain accurate solutions to the considered problems. Note that exact solutions are often not available, so they need to be approximated using some methods, such as the Adomian decomposition method.

scholarly journals Adomian Decomposition Method for a Class of Nonlinear Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
J. A. Sánchez Cano
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Coupled System ◽  
Nonlinear Ordinary Differential Equations ◽  
Adomian Decomposition

The Adomian decomposition method together with some properties of nested integrals is used to provide a solution to a class of nonlinear ordinary differential equations and a coupled system.

scholarly journals A New Improved Adomian Decomposition Method for Solving Emden{Fowler Type Equations of Higher{Order

2020 ◽  
pp. 9-17
Author(s):  
Zainab Ali Abdu AL-Rabahi ◽  
Yahya Qaid Hasan
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Linear Problems ◽  
Suggested Modification

In this paper, we present a suggested modification for Adomain decomposition method to solve Emden{Fowler Types Equations of higher-order ordinary differential equations. The proposed method can be applied to linear and non-linear problems. By using some illustrative examples, we tested the reliability and effectiveness of the proposed method and we found that the obtained results approximate the exact solution. Thus, we can conclude that this proposed method is efficient and reliable .

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