Higher order numeric solutions of the Lane–Emden-type equations derived from the multi-stage modified Adomian decomposition method

2015 ◽  
Vol 94 (1) ◽  
pp. 197-215 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Randolph Rach ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Modified Adomian Decomposition Method ◽  
Multi Stage ◽  
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.

Modified Adomian decomposition method for solving fractional optimal control problems

2017 ◽  
Vol 40 (6) ◽  
pp. 2054-2061 ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems

In this study, we use the modified Adomian decomposition method to solve a class of fractional optimal control problems. The performance index of a fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamical system is expressed in terms of a Caputo type fractional derivative. Some properties of fractional derivatives and integrals are used to obtain Euler–Lagrange equations for a linear tracking fractional control problem and then, the modified Adomian decomposition method is used to solve the resulting fractional differential equations. This technique rapidly provides convergent successive approximations of the exact solution to a linear tracking fractional optimal control problem. We compare the proposed technique with some numerical methods to demonstrate the accuracy and efficiency of the modified Adomian decomposition method by examining several illustrative test problems.

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