scholarly journals Application of Adomian Decomposition Method to Solving Higher Order Singular Value Problems for Ordinary Differential Equations

2020 ◽  
pp. 22-28
Author(s):  
Yahya Qaid Hasan ◽  
Somaia Ali Alaqel
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Higher Order ◽  
Singular Value ◽  
Order Ordinary Differential Equation ◽  
Numerical Examples ◽  
Adomian Decomposition

This paper is an attempt to solve singular value problems for higher order ordinary differential equation by using new modification of Adomian Decomposition Method (ADM). Convergent series solution of considered problem have been obtained. Three numerical examples are discussed to validate the strength and ease of the method used.

scholarly journals Sumudu Decomposition Method for Solving Fractional Bratu-Type Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 585-605
Author(s):  
N. B. Manjare ◽  
H. T. Dinde
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Type Differential Equation

The purpose of this paper is to introduce Sumudu decomposition method for solving Fractional Bratu-type differential equation. This method is a combination of the Sumudu transform and Adomian decomposition method. The fractional derivative is described in the Caputo sense. The Sumudu decomposition method is applied to obtain approximate analytical solution of non-linear Fractional Bratu-type differential equation. A novel combination of Sumudu transform and Adomian decomposition provides approximate solution in the form of infinite convergent series solution. The behavior of approximate analytical solutions and exact solutions for different values of α are plotted graphically. The results acquired from Sumudu decomposition method indicates that the proposed method is very well founded, suitable and effective. Finally, some numerical examples are given to illustrate the efficiency and applicability of our method.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

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 Adomian method for solving Emden-Fowler equation of higher order

2020 ◽  
pp. 231-240
Author(s):  
Nuha Mohammed Dabwan ◽  
Yahya Qaid Hasan
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Adomian Method ◽  
Fowler Equation

Adomian Decomposition Method (ADM) is presented in this article to solve Emden-Fowler equation of higher order. We tested this method with several numerical examples that showed the reliability of the method in the finding of good approximate solutions.

scholarly journals An accelerated solution for some classes of nonlinear partial differential equations

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
I. L. El-Kalla ◽  
E. M. Mohamed ◽  
H. A. A. El-Saka
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Numerical Examples ◽  
Adomian Decomposition

AbstractIn this paper, we apply an accelerated version of the Adomian decomposition method for solving a class of nonlinear partial differential equations. This version is a smart recursive technique in which no differentiation for computing the Adomian polynomials is needed. Convergence analysis of this version is discussed, and the error of the series solution is estimated. Some numerical examples were solved, and the numerical results illustrate the effectiveness of this version.

scholarly journals Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Xiang-Chao Shi ◽  
Lan-Lan Huang ◽  
Zhen-Guo Deng ◽  
Dan Liu
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Decomposition Method ◽  
Order Approximation ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Nonlinear Fractional Differential Equation ◽  
Adomian Decomposition ◽  
Engineering Problems ◽  
Fractional Differential

Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.

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 Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

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