scholarly journals Mathematical Modelling in Engineering with Integral Transforms via Modified Adomian Decomposition Method

2021 ◽  
Vol 8 (3) ◽  
pp. 409-417
Author(s):  
Minakshi Mohanty ◽  
Saumya Ranjan Jena ◽  
Satya Kumar Misra
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Integral Transforms ◽  
Physical Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Different Types ◽  
Linear Differential ◽  
Homogeneous Linear

In this work three integral transforms through modified Adomian decomposition method (ADM) are proposed to obtain the approximate analytical solution of different types of mathematical models arising in physical problems. These transformations are applied for both homogeneous and non-homogeneous linear differential equations. The efficiency and accuracy of the proposed methods are implemented through higher order non-homogeneous ordinary differential equations. Numerical tests are reported for applicability of the current scheme based on different transformations and compared with exact solutions.

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 Solving Ordinary Differential Equation of Higher Order by Adomian Decomposition Method

2020 ◽  
pp. 44-53
Author(s):  
Sumayah Ghaleb Othman ◽  
Yahya Qaid Hasan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Different Types

Aims/ Objectives: In this article, we use Adomian Decomposition method (ADM) for solving initial value problems in the higher order ordinary differential equations. Many researchers have used the ADM in order to find convergent as well as exact solutions of different types of equations. Therefore, the ADM is considered as an effective and successful method for solving differential equations. In this paper, we presented some suggested amendments to the ADM by using a new differential operator in order to find solutions for higher order types of equations. We demonstrated the effectiveness of this method through many examples and we find out that we get an approximate solutions using the proposed amendments. We can conclude that the suggested modification of ADM is afftective and produces reliable results.

scholarly journals Modified Adomian Decomposition Method for the Solution of Integro-Differential Equations

2021 ◽  
pp. 111-124
Author(s):  
R. O. Ijaiya ◽  
O. A. Taiwo ◽  
K. A. Bello
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Polynomials ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Canonical Polynomials

This paper is concerned with modification of the Adomian Decomposition Method for solving linear and non-linear Volterra and Volterra-Fredholm Integro-Differential equations. The Modified form of ADM was carried out by replacing the Adomian polynomials constructed in the conventional Adomian Decomposition Method with the constructed canonical polynomials. The modified Adomian Decomposition Method was applied to solve some existing example. The results obtained using the newly modified ADM proved superior when compared with the conventional ADM.

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