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 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 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.

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)

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.

scholarly journals Some Probability Characteristics Functions of the Solution of a Stochastic Non-Linear Fredholm Integral Equation of the Second Kind

2011 ◽  
Vol 8 (2) ◽  
pp. 394-399
Author(s):  
Baghdad Science Journal
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Spectral Density ◽  
Probability Density ◽  
Fredholm Integral Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Non Linear

In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)

scholarly journals Computation of semi-analytical solutions of fuzzy nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zia Ullah ◽  
Aman Ullah ◽  
Kamal Shah ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Decomposition Method ◽  
Nonlinear Integral Equation ◽  
Adomian Decomposition Method ◽  
Main Theme ◽  
Parametric Form ◽  
Nonlinear Integral Equations ◽  
Adomian Decomposition ◽  
Nonlinear Fredholm Integral Equation

Abstract In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A hybrid method of Laplace transform coupled with Adomian decomposition method is used to find the solution of the fuzzy nonlinear integral equations including fuzzy nonlinear Fredholm integral equation, fuzzy nonlinear Volterra integral equation, and fuzzy nonlinear singular integral equation of Abel type kernel. We also provide some suitable examples to better understand the proposed method.

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