Solution of nonlinear equations by modified adomian decomposition method

2002 ◽  
Vol 132 (1) ◽  
pp. 167-172 ◽  
Author(s):  
E. Babolian ◽  
J. Biazar
Keyword(s):  
Nonlinear Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

scholarly journals Comparison of the Adomian Decomposition Method and Regular Perturbation Method on Nonlinear Equations Second Kind of Volterra

2021 ◽  
Vol 14 (3) ◽  
pp. 1044-1056
Author(s):  
Rasmane Yaro ◽  
Bakari Abbo ◽  
Bassono Francis ◽  
Youssouf Pare
Keyword(s):  
Perturbation Method ◽  
Nonlinear Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Regular Perturbation ◽  
General Integral ◽  
Adomian Decomposition

In this paper, we study convergence of Adomian decomposition method applied tosecond kind Volterra general integral and show that this method and regular perturbation method converges to the same solution.

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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