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Article | Open Access

Application of Hybrid Bernstein Polynomials and Block-Pulse Functions for Solving Nonlinear Fuzzy Fredholm Integral Equations

Mahdi Baghmisheh1, Reza Ezzati2( )
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz 51579-44533, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj 31499-68111, Iran
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Abstract

In this paper, hybrid Bernstein polynomials and block-pulse functions based on the method of successive approximations are applied to obtain the approximate solution of nonlinear fuzzy Fredholm integral equations. The main idea of using the proposed method is that fuzzy integral in any iterative process will be reduced to the crisp integration. Some results concerning the error estimate and stability of the numerical method are presented. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method.

Keywords

fuzzy functionnonlinear fuzzy integral equationsiterative procedurehybrid functionBernstein polynomialsblock-pulse functions

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Fuzzy Information and Engineering
Volume 15 Issue 1,
March 2023
Pages 69-86
DOI: 10.26599/FIE.2023.9270006
Cite this article:
Baghmisheh M, Ezzati R. Application of Hybrid Bernstein Polynomials and Block-Pulse Functions for Solving Nonlinear Fuzzy Fredholm Integral Equations. Fuzzy Information and Engineering, 2023, 15(1): 69-86. https://doi.org/10.26599/FIE.2023.9270006

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Received: 15 June 2019
Revised: 02 December 2022
Accepted: 15 January 2023
Published: 01 March 2023
© The Author(s) 2023. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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