scholarly journals Analytical Solution of Nonlinear Dynamics of a Self-Igniting Reaction-Diffusion System Using Modified Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Felicia Shirly Peace ◽  
Narmatha Sathiyaseelan ◽  
Lakshmanan Rajendran
Keyword(s):  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Adomian Decomposition Method ◽  
Reaction Diffusion ◽  
Lewis Number ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Steady State Condition ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method) is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le) and parametersβ,γ, andϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.

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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