Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations

Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations

We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature fo...

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Main Authors: S. M. Sadatrasoul, R. Ezzati
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/413570
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spelling doaj-ce1a8a69ad194442994b57bb482b6e3d2020-11-24T21:05:33ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/413570413570Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral EquationsS. M. Sadatrasoul0R. Ezzati1Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, IranDepartment of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, IranWe introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2), and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.http://dx.doi.org/10.1155/2014/413570
collection DOAJ
language English
format Article
sources DOAJ
author S. M. Sadatrasoul
R. Ezzati
spellingShingle S. M. Sadatrasoul
R. Ezzati
Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations
Abstract and Applied Analysis
author_facet S. M. Sadatrasoul
R. Ezzati
author_sort S. M. Sadatrasoul
title Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations
title_short Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations
title_full Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations
title_fullStr Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations
title_full_unstemmed Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations
title_sort quadrature rules and iterative method for numerical solution of two-dimensional fuzzy integral equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2), and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.
url http://dx.doi.org/10.1155/2014/413570
work_keys_str_mv AT smsadatrasoul quadraturerulesanditerativemethodfornumericalsolutionoftwodimensionalfuzzyintegralequations
AT rezzati quadraturerulesanditerativemethodfornumericalsolutionoftwodimensionalfuzzyintegralequations
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