Abstract
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.
Highlights
Integral equations have some applications in different fields, such as physics, biological models, and so on [1,2,3,4,5]
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]
The primary aim of this paper is to extend the application of the sinc method together with double exponential (DE) transformation to find the approximate solution of 2D-FFIE
Summary
Integral equations have some applications in different fields, such as physics, biological models, and so on [1,2,3,4,5]. In [22], the sinc method was proposed to solve one-dimensional fuzzy integral equations. 6. Definition 2.1 (see [31]) A fuzzy number is a function u : R → [0, 1] satisfying the following properties:. Definition 2.4 (see [35]) If for every ε > 0, there exists δ > 0 such that D(f (x), f (x0)) < ε whenever x ∈ [a, b], |x – x0| < δ, the fuzzy real-valued function f : [a, b] → R is referred to as continuous at the point x0 ∈ [a, b]. According to the Nyström method in [40], we obtain an approximate solution of Eq (10) at arbitrary points as follows: uNM(x, y) = f (x, y) ⊕ λh1h2.
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