Numerical solution of two-dimensional fuzzy Fredholm integral equations of the second kind using triangular functions

Mirzaee, Farshid; Yari, Mohammad Komak; Hadadiyan, Elham

doi:10.1016/j.bjbas.2015.05.003

Cited by 12 publications

(15 citation statements)

References 15 publications

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“…Consider the following FFIE-2 with [19] fðx; rÞ ¼ ðr 2 þ rÞðsin x 2 À 0:05sinðxÞð1 À sinð1ÞÞÞ; fðx; rÞ ¼ ð4 À r 3 À rÞðsin x 2 À 0:05sinðxÞð1 À sinð1ÞÞÞ; and kðx; tÞ ¼ 0:1sinðxÞsin t 2 ; 0 6 x; t 6 1 and k ¼ 1:…”

Section: The Convergence Of the Methodsmentioning

confidence: 99%

Numerical solution of Fredholm fuzzy integral equations of the second kind using hybrid of block-pulse functions and Taylor series

Mirzaee

2014

Ain Shams Engineering Journal

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In this paper, we present a numerical method based on an NM-set of general hybrid of block-pulse function and Taylor series (HBT), to solve linear Fredholm fuzzy integral equations of the second kind (FFIE-2). Moreover, the convergence of the proposed method is given. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving these equations.Ó 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

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Section: The Convergence Of the Methodsmentioning

confidence: 99%

Numerical solution of Fredholm fuzzy integral equations of the second kind using hybrid of block-pulse functions and Taylor series

Mirzaee

2014

Ain Shams Engineering Journal

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“…One of the first applications of fuzzy integration was given by Wu and Ma [5], who investigated the fuzzy Fredholm integral equation of the second kind (FFIE-2). This work which established the existence of a unique solution for (FFIE-2) was followed by other works such as Mirzaee et al [6] and Nguyen [7] where an original fuzzy differential equation is replaced by a fuzzy integral equation. Recently Liao, in his Ph.D. thesis [8], has proposed the homotopy analysis method (HAM) to solve some classes of nonlinear equations.…”

Section: Introductionmentioning

confidence: 90%

Solving linear and nonlinear Abel fuzzy integral equations by homotopy analysis method

Mirzaee

Yari

Paripour

2015

Journal of Taibah University for Science

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The main purpose of this article is to present an approximation method for solving Abel fuzzy integral equation in the most general form. The proposed approach is based on homotopy analysis method. This method transforms linear and nonlinear Abel fuzzy integral equations into two crisp linear and nonlinear integral equations. The convergence analysis for the proposed method is also introduced. We give some numerical applications to show efficiency and accuracy of the method. All of the numerical computations have been performed on a computer with the aid of a program written in Matlab.

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“…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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Numerical solution of two-dimensional fuzzy Fredholm integral equations of the second kind using triangular functions

Cited by 12 publications

References 15 publications

Numerical solution of Fredholm fuzzy integral equations of the second kind using hybrid of block-pulse functions and Taylor series

Numerical solution of Fredholm fuzzy integral equations of the second kind using hybrid of block-pulse functions and Taylor series

Solving linear and nonlinear Abel fuzzy integral equations by homotopy analysis method

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

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