Abstract
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.
Highlights
Many authors proposed various numerical methods for solving one-dimensional fuzzy integral equations [1,2,3,4,5,6,7,8,9]
Two-dimensional fuzzy integral equations have been noticed by a lot of researchers because of their broad applications in engineering sciences
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]
Summary
Many authors proposed various numerical methods for solving one-dimensional fuzzy integral equations [1,2,3,4,5,6,7,8,9]. 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]. In this paper, we want to solve 2DLFFIEs by applying two-dimensional fuzzy Lagrange interpolation and iterative method. We propose two-dimensional fuzzy Lagrange interpolation and iterative method for solving 2DLFFIEs. In Section 4, we verify convergence analysis for proposed method.
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