A Comparison Study Between a Chebyshev Collocation Method and the Adomian Decomposition Method for Solving Linear System of Fredholm Integral Equations of the Second Kind

2012 ◽  
Vol 24 (1) ◽  
pp. 49-59 ◽  
Author(s):  
H. Bakodah
Keyword(s):  
Linear System ◽  
Integral Equations ◽  
Collocation Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fredholm Integral Equations ◽  
Comparison Study ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Adomian Decomposition

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.

Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation

2018 ◽  
Vol 85 (1-2) ◽  
pp. 53 ◽  
Author(s):  
Ahmed A. Hamoud ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fredholm Integral Equations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Uniqueness Of The Solution ◽  
Fuzzy Solution

In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

scholarly journals Numerical Solution of Nonlinear Fredholm Integral Equations by Using NKM and ADM

2017 ◽  
Vol 65 (1) ◽  
pp. 61-66
Author(s):  
MM Hasan ◽  
MA Matin
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fredholm Integral Equations ◽  
Quadrature Method ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Nonlinear Fredholm Integral Equations

In this paper, we present a numerical method to solve a non-linear Fredholm integral equations. We intend to approximate the solution of this equation by Newton-Kantorovich-quadrature method and Adomian Decomposition method compare both the methods accurately for solving the non-linear Fredholm integral equation. Dhaka Univ. J. Sci. 65(1): 61-66, 2017 (January)

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 A Study of Some Iterative Methods for Solving Fuzzy Volterra-Fredholm Integral Equations

2018 ◽  
Vol 11 (3) ◽  
pp. 1228 ◽  
Author(s):  
Ahmed A. Hamoud ◽  
Ali Dhurgham Azeez ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fredholm Integral Equations ◽  
Analysis Method ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Fuzzy Solution

<div>This paper mainly focuses on the recent advances in the some approximated methods for solving fuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, variational iteration method and homotopy analysis method. We converted fuzzy Volterra-Fredholm integral equation to a system of Volterra-Fredholm integral equation in crisp case. The approximated methods using to find the approximate solutions of this system and hence obtain an approximation for the fuzzy solution of the fuzzy Volterra-Fredholm integral equation. To assess the accuracy of each method, algorithms with Mathematica 6 according is used. Also, some numerical examples are included to demonstrate the validity and applicability</div><div>of the proposed techniques.</div>This paper mainly focuses on the recent advances in the some approximated methods for solvingfuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, variational iterationmethod and homotopy analysis method. We converted fuzzy Volterra-Fredholm integral equation to asystem of Volterra-Fredholm integral equation in crisp case. The approximated methods using to find theapproximate solutions of this system and hence obtain an approximation for the fuzzy solution of the fuzzyVolterra-Fredholm integral equation. To assess the accuracy of each method, algorithms with Mathematica 6according is used. Also, some numerical examples are included to demonstrate the validity and applicabilityof the proposed techniques.

The modified Adomian decomposition method and the noise terms phenomenon for solving nonlinear weakly-singular Volterra and Fredholm integral equations

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Abdul-Majid Wazwaz ◽  
Randolph Rach ◽  
Jun-Sheng Duan
Keyword(s):  
Integral Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
The Self ◽  
Fredholm Integral Equations ◽  
Weakly Singular ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

AbstractIn this paper, we use the systematic modified Adomian decomposition method (ADM) and the phenomenon of the self-canceling ”noise” terms for solving nonlinear weakly-singular Volterra, Fredholm, and Volterra-Fredholm integral equations. We show that the proposed approach minimizes the computation, when compared with other conventional schemes. Our results are validated by investigating several examples.

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