Numerical Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind Using Fuzzy Haar Wavelet

Ziari, Shokrollah; Ezzati, Reza; Abbasbandy, Saeid

doi:10.1007/978-3-642-31718-7_9

Cited by 32 publications

(8 citation statements)

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“…The analytic-numeric methods like Adomian decomposition, homotopy analysis and homotopy perturbation are used in [2,4,5,26,27,29]. Other techniques used in the construction of the numerical methods for fuzzy integral equations are: quadrature rules and Nyström techniques (see [1] and [25]), Lagrange and splines interpolation (see [3] and [23]), divided and finite differences (see [32]), Bernstein polynomials (see [15] and [31]), Chebyshev interpolation (see [8]), Legendre wavelets (see [21]), fuzzy Haar wavelets (see [38]), and Galerkin type techniques (see [28]). …”

Section: Introductionmentioning

confidence: 99%

Approximating the solution of nonlinear Hammerstein fuzzy integral equations

Bica

Popescu

2014

Fuzzy Sets and Systems

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Section: Introductionmentioning

confidence: 99%

Approximating the solution of nonlinear Hammerstein fuzzy integral equations

Bica

Popescu

2014

Fuzzy Sets and Systems

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“…The analytic-numeric methods like Adomian decomposition, homotopy analysis are used in [1,5,22,24]. For review of other techniques see [4,14,21,23,30,37]. Since many problems in engineering and applied sciences that can be put in the form the form of two-dimensional fuzzy integral equations, it is important to we develop numerical methods for solving such integral equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of two-dimensional nonlinear Hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula

Sadatrasoul

Ezzati

2016

Journal of Computational and Applied Mathematics

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Please cite this article as: S.M. Sadatrasoul, R. Ezzati, Numerical solution of two-dimensional nonlinear Hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractIn this paper, our aim is to provide an efficient iterative method of successive approximations to approximate solution of linear and nonlinear two-dimensional Hammerstein fuzzy integral equations by defining and developing an optimal quadrature formula for classes of two-dimensional fuzzy-number-valued functions of Lipschitz type. After the introduction of the optimal formula, we prove the convergence of the method of successive approximations used to approximate the solution of two-dimensional Hammerstein fuzzy integral equations and investigate the numerical stability of the presented method with respect to the choice of the first iteration. Finally, some illustrative numerical experiments confirm the theoretical results and demonstrate the accuracy of the method.Keywords: Two dimensional Hammerstein fuzzy integral equations (2DHFIE); Optimal quadrature formula; Banach fixed point theorem; The method of successive approximations; Iterative method.

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“…Up to present, these methods apply quadrature formulas (see [17], [18]), Nyström techniques (see [1]), Adomian decomposition (see [2], [5]), iterative techniques and successive approximations (see [8], [9], [10], [14], [15], [17] and [29]). In other numerical methods for fuzzy integral equations are involved Bernstein polynomials (see [13] and [27]), Galerkin techniques (see [23]), Lagrange interpolation (see [16]), homotopy analysis (see [24]), homotopy perturbation (see [22]), divided and finite differences (see [28]), Legendre (see [32]) and Haar wavelets (see [35]). Recently, in [10], Bica and Popescu developed an iterative numerical method to solve nonlinear fuzzy Hammerstein-Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 99%