Error estimation and numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using triangular functions

Baghmisheh, Mahdi; Ezzati, Reza

doi:10.3233/ifs-151783

Cited by 17 publications

(2 citation statements)

References 39 publications

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“…[0, 1) Definition 3.2 [35] Hybrid orthonormal block-pulse functions and Bernstein polynomials are defined on the interval as follows:…”

Section: Preliminarymentioning

confidence: 99%

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

Baghmisheh¹,

Ezzati²

2023

Fuzzy Information and Engineering

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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.

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“…[0, 1) Definition 3.2 [35] Hybrid orthonormal block-pulse functions and Bernstein polynomials are defined on the interval as follows:…”

Section: Preliminarymentioning

confidence: 99%

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

Baghmisheh¹,

Ezzati²

2023

Fuzzy Information and Engineering

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“…Ezzati and Ziari [8] suggested an iterative procedure via the trapezoidal rule to solve fuzzy Fredholm integral equations, and also proved the convergence of the proposed method. Baghmisheh and Ezzati investigated the error estimation and numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using triangular functions [17]. In [16], authors presented a numerical method based on the iterative method and midpoint quadrature formula for solving linear fuzzy Fredholm integral equations of the second kind.…”

Section: Introductionmentioning

confidence: 99%

New error estimation based on midpoint iterative method for solving nonlinear fuzzy fredholm integral equations

Samadpour

Ezzati

2019

Filomat

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In this paper, first, we apply the successive approximations method in terms of midpoint quadrature formula to solve nonlinear fuzzy Fredholm integral equations of the second kind (NFFIE-2). Considering some assumptions, we acquire a new error estimation. Moreover, we prove the convergence of the proposed method. Then, we study the numerical stability of the proposed method with respect to the first iteration choice. Eventually, to demonstrate the accuracy of the suggested method, we present two numerical examples.

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The Fuzzy Integral Evaluation Method Based on Feature Weighting for the Level of Complex Social Development

Zhu

2019

Cyberspace Safety and Security

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Error estimation and numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using triangular functions

Cited by 17 publications

References 39 publications

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

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

New error estimation based on midpoint iterative method for solving nonlinear fuzzy fredholm integral equations

The Fuzzy Integral Evaluation Method Based on Feature Weighting for the Level of Complex Social Development

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