Publication:
An improved numerical iterative method for solving nonlinear fuzzy Fredholm integral equations via Picard’s method and generalized quadrature rule

Simple item page
dc.contributor.authorZiari, Shokrollah
dc.contributor.authorAllahviranloo, Tofigh A.
dc.contributor.authorPedrycz, Witold
dc.contributor.institutionZiari, Shokrollah, Department of Mathematics, Islamic Azad University, Tehran, Iran
dc.contributor.institutionAllahviranloo, Tofigh A., Faculty of Engineering and Natural Sciences, Bahçeşehir Üniversitesi, Istanbul, Turkey
dc.contributor.institutionPedrycz, Witold, University of Alberta, Edmonton, Canada
dc.date.accessioned2025-10-05T15:30:17Z
dc.date.issued2021
dc.description.abstractIn this paper, we approximate the integral of fuzzy-number-valued functions using generalized quadrature rule and obtain its error estimate. Utilizing the generalized quadrature rule and successive approximations method, we construct an iterative approach to find the numerical approximation of solutions. Moreover, we investigate the error analysis of the numerical method, which guarantees pointwise convergence. Then we apply the presented method to two numerical experiments to present the accuracy and convergence of the method. © 2022 Elsevier B.V., All rights reserved.
dc.identifier.doi10.1007/s40314-021-01616-1
dc.identifier.issn18070302
dc.identifier.issn22383603
dc.identifier.issue6
dc.identifier.scopus2-s2.0-85113739468
dc.identifier.urihttps://doi.org/10.1007/s40314-021-01616-1
dc.identifier.urihttps://hdl.handle.net/20.500.14719/9471
dc.identifier.volume40
dc.language.isoen
dc.publisherSpringer Science and Business Media Deutschland GmbH
dc.relation.sourceComputational and Applied Mathematics
dc.subject.authorkeywords46s40
dc.subject.authorkeywords47s40
dc.subject.authorkeywordsFuzzy Fredholm Integral Equations
dc.subject.authorkeywordsGeneralized Quadrature Rule
dc.subject.authorkeywordsIterative Numerical Method
dc.subject.authorkeywordsLipschitz Condition
dc.subject.authorkeywordsPicard Iteration Method
dc.subject.authorkeywordsApproximation Theory
dc.subject.authorkeywordsConvergence Of Numerical Methods
dc.subject.authorkeywordsFredholm Integral Equations
dc.subject.authorkeywordsFuzzy Sets
dc.subject.authorkeywordsIterative Methods
dc.subject.authorkeywords46s40
dc.subject.authorkeywords47s40
dc.subject.authorkeywordsFuzzy Fredholm Integral Equations
dc.subject.authorkeywordsGeneralized Quadrature Rule
dc.subject.authorkeywordsIteration Method
dc.subject.authorkeywordsIterative Numerical Method
dc.subject.authorkeywordsLipschitz Conditions
dc.subject.authorkeywordsPicard Iteration
dc.subject.authorkeywordsPicard Iteration Method
dc.subject.authorkeywordsQuadrature Rules
dc.subject.authorkeywordsNonlinear Equations
dc.subject.indexkeywordsApproximation theory
dc.subject.indexkeywordsConvergence of numerical methods
dc.subject.indexkeywordsFredholm integral equations
dc.subject.indexkeywordsFuzzy sets
dc.subject.indexkeywordsIterative methods
dc.subject.indexkeywords46s40
dc.subject.indexkeywords47s40
dc.subject.indexkeywordsFuzzy fredholm integral equations
dc.subject.indexkeywordsGeneralized quadrature rule
dc.subject.indexkeywordsIteration method
dc.subject.indexkeywordsIterative numerical method
dc.subject.indexkeywordsLipschitz conditions
dc.subject.indexkeywordsPicard iteration
dc.subject.indexkeywordsPicard iteration method
dc.subject.indexkeywordsQuadrature rules
dc.subject.indexkeywordsNonlinear equations
dc.titleAn improved numerical iterative method for solving nonlinear fuzzy Fredholm integral equations via Picard’s method and generalized quadrature rule
dc.typeArticle
dcterms.referencesAbbasbandy, Saied, The Adomian decomposition method applied to the Fuzzy system of Fredholm integral equations of the second kind, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14, 1, pp. 101-110, (2006), Abbasbandy, Saied, Numerical method for solving linear Fredholm fuzzy integral equations of the second kind, Chaos, Solitons and Fractals, 31, 1, pp. 138-146, (2007), Allahviranloo, Tofigh A., Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations, Iranian Journal of Fuzzy Systems, 12, 2, pp. 75-86, (2015), Fuzzy Mathematics Approximation Theory, (2010), J Fuzzy Math, (2001), Fariborzi Araghi, Mohammad Ali, Numerical solution of fuzzy Fredholm integral equations by the Lagrange interpolation based on the extension principle, Soft Computing, 15, 12, pp. 2449-2456, (2011), Fuzzy Inf Eng, (2011), Babolian, Esmaeil, Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method, Applied Mathematics and Computation, 161, 3, pp. 733-744, (2005), Baghmisheh, Mahdi, Numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using hybrid of block-pulse functions and Taylor series, Advances in Difference Equations, 2015, 1, (2015), Baghmisheh, Mahdi, Error estimation and numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using triangular functions, Journal of Intelligent and Fuzzy Systems, 30, 2, pp. 639-649, (2016)
dspace.entity.typePublication
local.indexed.atScopus
person.identifier.scopus-author-id37082493600
person.identifier.scopus-author-id8834494700
person.identifier.scopus-author-id56854903200

Files

Collections

Scopus İndeksli Yayınlar Koleksiyonu