scholarly journals EXACT AND APPROXIMATE ANALYTIC SOLUTIONS OF THE JEFFERY-HAMEL FLOW PROBLEM BY THE DUAN-RACH MODIFIED ADOMIAN DECOMPOSITION METHOD

2016 ◽  
Vol 21 (2) ◽  
pp. 174-187 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Samy Mziou ◽  
Randolph C. Rach
Keyword(s):  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Boundary ◽  
Flow Problem ◽  
Adomian Decomposition Method ◽  
Analytic Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).

scholarly journals Adomian Decomposition Method for a Nonlinear Heat Equation with Temperature Dependent Thermal Properties

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Ghulam Mohammad ◽  
M. T. Mustafa ◽  
F. D. Zaman
Keyword(s):  
Exact Solution ◽  
Heat Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Nonlinear Heat Equation ◽  
Temperature Dependent ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Method Analysis

The solutions of nonlinear heat equation with temperature dependent diffusivity are investigated using the modified Adomian decomposition method. Analysis of the method and examples are given to show that the Adomian series solution gives an excellent approximation to the exact solution. This accuracy can be increased by increasing the number of terms in the series expansion. The Adomian solutions are presented in some situations of interest.

scholarly journals Solution of Two-Point Linear and Nonlinear Boundary Value Problems with Neumann Boundary Conditions Using a New Modified Adomian Decomposition Method

2020 ◽  
pp. 49-60
Author(s):  
Justina Mulenga ◽  
Patrick Azere Phiri
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Value Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

In this paper, we present the New Modified Adomian Decomposition Method which is a modification of the Modified Adomian Decomposition Method. The new method incorporates the inverse linear operator theorem into the modified Adomian decomposition method for the calculation of u0. Six linear and nonlinear boundary value problems with Neumann conditions are solved in order to test the method. The results show that the method is effective.

Solution of the Magnetohydrodynamics Jeffery-Hamel Flow Equations by the Modified Adomian Decomposition Method

2015 ◽  
Vol 7 (5) ◽  
pp. 675-686 ◽  
Author(s):  
Lei Lu ◽  
Junsheng Duan ◽  
Longzhen Fan
Keyword(s):  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Hartmann Number ◽  
Adomian Decomposition Method ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Equations ◽  
Analytical Approximations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

AbstractIn this paper, the nonlinear boundary value problem (BVP) for the Jeffery-Hamel flow equations taking into consideration the magnetohydrodynamics (MHD) effects is solved by using the modified Adomian decomposition method. We first transform the original two-dimensional MHD Jeffery-Hamel problem into an equivalent third-order BVP, then solve by the modified Adomian decomposition method for analytical approximations. Ultimately, the effects of Reynolds number and Hartmann number are discussed.

scholarly journals Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method

2020 ◽  
pp. 105-113
Author(s):  
Joel Ndam ◽  
O. Adedire
Keyword(s):  
Taylor Series ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytic Method ◽  
Series Method ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Taylor Series Method

In this paper, we compare the solution of the van der Pol equation obtained by using the truncated Taylor series method and the modified Adomian decomposition method with the solution obtained by the Poincare-Lindstedt (P-L) method. The approximating 4-component modified Adomian decomposition method behaves more like an approximate P-L analytic method than the tenth-order Taylor series. Also, with the addition of just one term, the approximating 5-component modified Adomian decomposition method produces a more convergent solution to that of P-L analytic method than the twenty second-order Taylor series approximation as the independent variable t representing time progressively increases. A general comparison of the two solutions revealed that the absolute errors generated by the approximating polynomial from the Taylor series are greater than the ones generated from the modified Adomian decomposition method. It was further revealed that very few components of the modified Adomian decomposition could yield a series of about 3 times the order of the one obtained by using the Taylor series method. Hence, we recommend the inclusion of the modified Adomian Decomposition Method in modern mathematical tools.

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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