Iterative method for numerical solution of two-dimensional nonlinear fuzzy integral equations

Sadatrasoul, Seyed Mahdi; Ezzati, Reza

doi:10.1016/j.fss.2014.12.008

Cited by 28 publications

(7 citation statements)

References 33 publications

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“…Rivaz et al [24] and Ezzati et al [25] presented the homotopy perturbation method and fuzzy bivariate Bernestein polynomials method to solve 2D-FFIE, respectively. Other noticeable methods applied to 2D-FFIE were the block-pulse functions [26], triangular functions method [27], cubature method [28], and iterative method [29,30].…”

Section: Introductionmentioning

confidence: 99%

Solving two-dimensional fuzzy Fredholm integral equations via sinc collocation method

Zhang

2020

Adv Differ Equ

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In this paper, we present a numerical method to solve two-dimensional fuzzy Fredholm integral equations (2D-FFIE) by combing the sinc method with double exponential (DE) transformation. Using this method, the fuzzy Fredholm integral equations are converted into dual fuzzy linear systems. Convergence analysis is performed in terms of the modulus of continuity. Numerical experiments demonstrate the efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Solving two-dimensional fuzzy Fredholm integral equations via sinc collocation method

Zhang

2020

Adv Differ Equ

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“…Based on this trend, the iterative procedure based on quadrature formula is described in [27,37], while the successive approximations procedure is presented in [19,20]. The numericalanalytical procedures to solve fuzzy integral equations including fuzzy Laplace transform method [36], homotopy analysis method [39], fuzzy differential transform method [32], Adomian decomposition method [38], finite differences method [15] and variational iteration method [34] are also applied. Other numerical techniques developed for fuzzy integral equations based on fuzzy Haar wavelets, Legendre wavelets, Legendre and Chebyshev interpolations, Galerkin, triangular and block-pulse functions can be found in [16,18,21,28,31].…”

Section: Introductionmentioning

confidence: 99%

Reliable numerical algorithm for handling fuzzy integral equations of second kind in Hilbert spaces

Al‐Smadi

2019

Filomat

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Integral equations under uncertainty are utilized to describe different formulations of physical phenomena in nature. This paper aims to obtain analytical and approximate solutions for a class of integral equations under uncertainty. The scheme presented here is based upon the reproducing kernel theory and the fuzzy real-valued mappings. The solution methodology transforms the linear fuzzy integral equation to crisp linear system of integral equations. Several reproducing kernel spaces are defined to investigate the approximate solutions, convergence and the error estimate in terms of uniform continuity. An iterative procedure has been given based on generating the orthonormal bases that rely on Gram-Schmidt process. Effectiveness of the proposed method is demonstrated using numerical experiments. The gained results reveal that the reproducing kernel is a systematic technique in obtaining a feasible solution for many fuzzy problems.

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“…Also, two-dimensional fuzzy integral equations have been noticed by a lot of researchers because of their broad applications in engineering sciences. Some of the most important papers in this area are trapezoidal quadrature rule and iterative method [10][11][12], triangular functions [13], quadrature iterative [14], Bernstein polynomials [15], collocation fuzzy wavelet like operator [16], homotopy analysis method (HAM) [17], open fuzzy cubature rule [18], kernel iterative method [19], modified homotopy pertubation [20], block-pulse functions [21], optimal fuzzy quadrature formula [22], and finally, iterative method and fuzzy bivariate block-pulse functions [23]. Also, some researchers have solved one-dimensional fuzzy Fredholm integral equations by using fuzzy interpolation via iterative method such as: iterative interpolation method [9], Lagrange interpolation based on the extension principle [5], and spline interpolation [7].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Two-Dimensional Linear Fuzzy Fredholm Integral Equations by the Fuzzy Lagrange Interpolation

Nouriani

Ezzati

2018

Advances in Fuzzy Systems

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In this study, at first, we propose a new approach based on the two-dimensional fuzzy Lagrange interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equation (2DLFFIE). Then, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm by two theorems. Finally, by some examples, we show the efficiency of the proposed method.

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Iterative method for numerical solution of two-dimensional nonlinear fuzzy integral equations

Cited by 28 publications

References 33 publications

Solving two-dimensional fuzzy Fredholm integral equations via sinc collocation method

Solving two-dimensional fuzzy Fredholm integral equations via sinc collocation method

Reliable numerical algorithm for handling fuzzy integral equations of second kind in Hilbert spaces

Numerical Solution of Two-Dimensional Linear Fuzzy Fredholm Integral Equations by the Fuzzy Lagrange Interpolation

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