The Solve of Fuzzy Integral Equation by using Quadrature Formula

Abstract

In this paper, we consider a new approach for solving fuzzy integral equation. In this work, we find an approximate solution of fuzzy integral equation by using fuzzy Gauss quadrature formula. We first express the necessary materials and definitions, and then we introduce the concept of fuzzy Gauss quadrature formula. In the last section, we present an important application of fuzzy Gauss quadrature rule to solve a boundary value problem. In this problem, the boundary conditions appear as the form of fuzzy integral equations. However, the integrals in the boundary conditions are approximated by fuzzy Gauss quadrature method. Numerical examples given in the last part confirm the accuracy and validity of our new technique. In this example, we obtain the Hausdorff distance between exact solution and approximate solution.