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 .

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

2021 ◽  
Vol 23 (1) ◽  
pp. 590
Author(s):  
Badran Jasim Salim ◽  
Oday Ahmed Jasim ◽  
Zeiad Yahya Ali
Keyword(s):  
Genetic Algorithm ◽  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Linear Partial Differential Equations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Optimal Value ◽  
Mean Square Errors

<p class="Char">In this paper, the modified Adomian decomposition method (MADM) is usedto solve different types of differential equations, one of the numerical analysis methods for solving non linear partial differential equations (Drinfeld–Sokolov–Wilson system) and short (DSWS) that occur in shallow water flows. A Genetic Algorithm was used to find the optimal value for the parameter (a). We numerically solved the system (DSWS) and compared the result to the exact solution. When the value of it is low and close to zero, the MADM provides an excellent approximation to the exact solution. As well as the lower value of leads to the numerical algorithm of (MADM) approaching the real solution.  Finally, found the optimal value when a=-10 by using the Genetic Algorithm (G-MADM). All the computations were carried out with the aid of Maple 18 and Matlab to find the parameter value (a) by using the genetic algorithm as well as to figures drawing. The errors in this paper resulted from cut errors and mean square errors.</p>

scholarly journals Exact Solution of Space-Time Fractional Partial Differential Equations by Adomian Decomposition Method

2021 ◽  
pp. 75-87
Author(s):  
Vidya N. Bhadgaonkar ◽  
Bhausaheb R. Sontakke
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
Physical Models ◽  
Partial Differential ◽  
Conduction Model ◽  
Adomian Decomposition ◽  
Present Technique

The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.

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