Solving linear fuzzy fredholm integral equations of the second kind via iterative method and simpson quadrature rule: A ReviewAtiyeh Mashhadi Gholam, Reza Ezzat (pp. 121-147)
Abstract.In this paper, first, we survey some methods to solve fuzzy Fredholm integral equation such as iterative trapezoidal quadrature rule, hybrid of block-pulse functions and Taylor series, iterative fuzzy wavelet like operator method. Then, we introduce a new method of successive approximations based on the Simpson quadrature rule for solving linear fuzzy Fredholm integral equations of the second kind (LFFIE-2). Moreover, we present the convergence analysis. Also, we present numerical stability analysis of the proposed method. Furthermore, we give a stopping criterion. Finally, to illustrate the applicability of the proposed method, we present some numerical tests.
Keywords:integral equation, iterative method, Simpson quadrature rule, convergence analysis, numerical stability analysis.