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.

Solutions of the modified Kawahara equation with time-and space-fractional derivatives

2016 ◽  
Vol 7 (1) ◽  
pp. 10 ◽  
Author(s):  
M. Safavi ◽  
A. A. Khajehnasiri
Keyword(s):  
Approximate Solution ◽  
Fractional Differential Equations ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Time And Space ◽  
Kawahara Equation ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we consider fractional differential equations (FDEs), specially modified Kawahara equation with time and space fractional derivatives, also we use Adomian decomposition method (ADM) to approximate the exact solutions of this equation. The ADM method converts the FKEs to an iterated formula that approximate solution is computable. The numerical examples illustrate efficiency and accuracy of the proposed method.

scholarly journals Approximate Solution of Systems of Volterra Integral Equations of Second Kind by Adomian Decomposition Method

2015 ◽  
Vol 63 (1) ◽  
pp. 15-18
Author(s):  
Md Shariful Islam ◽  
Mir Shariful Islam ◽  
Md Zavid Iqbal Bangalee ◽  
AFM Khodadad Khan ◽  
Amal Halder
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Integral Equations ◽  
Decomposition Method ◽  
Real Life ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Life Problems ◽  
Adomian Decomposition ◽  
Differential And Integral Equations

Real life problems that arise in different branches of science and social science, in the form of differential and integral equations are non-linear in nature. However, methods developed in Mathematics, usually, are suitable for the linear system. In this article, we talk on approximating solution of system of Volterra integral equations of second kind in an analytic way using Adomian decomposition method in Mathematica. DOI: http://dx.doi.org/10.3329/dujs.v63i1.21761 Dhaka Univ. J. Sci. 63(1): 15-18, 2015 (January)

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 Approximation Algorithm for a System of Pantograph Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sabir Widatalla ◽  
Mohammed Abdulai Koroma
Keyword(s):  
Approximate Solution ◽  
Approximation Algorithm ◽  
Laplace Transform ◽  
Numerical Algorithm ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
High Degree ◽  
Very High

We show how to adapt an efficient numerical algorithm to obtain an approximate solution of a system of pantograph equations. This algorithm is based on a combination of Laplace transform and Adomian decomposition method. Numerical examples reveal that the method is quite accurate and efficient, it approximates the solution to a very high degree of accuracy after a few iterates.

scholarly journals A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Lie-jun Xie
Keyword(s):  
Integral Equations ◽  
Nonlinear Equations ◽  
Decomposition Method ◽  
Taylor Expansion ◽  
Series Solution ◽  
New Technology ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

We propose a new modification of the Adomian decomposition method for Volterra integral equations of the second kind. By the Taylor expansion of the components apart from the zeroth term of the Adomian series solution, this new technology overcomes the problems arising from the previous decomposition method. The validity and applicability of the new technique are illustrated through several linear and nonlinear equations by comparing with the standard decomposition method and the modified decomposition method. The results obtained indicate that the new modification is effective and promising.

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 A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

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.

THE ADOMIAN DECOMPOSITION METHOD APPLIED TO THE FUZZY SYSTEM OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

2006 ◽  
Vol 14 (01) ◽  
pp. 101-110 ◽  
Author(s):  
S. ABBASBANDY ◽  
T. ALLAHVIRANLOO
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Fuzzy System ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fredholm Integral Equations ◽  
Extension Principle ◽  
Numerical Example ◽  
Adomian Decomposition

In this work, the Adomian decomposition(AD) method is applied to the Fuzzy system of linear Fredholm integral equations of the second kind(FFIE). First the crisp Fredholm integral equation is solved by AD method and then the crisp solution is fuzzified by extension principle. The proposed algorithm is illustrated by solving a numerical example.

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