On numerical solution of nonlinear fuzzy Urysohn-Volterra delay integral equations based on iterative method and trapezoidal quadrature rule

Abstract

In the present study, in the beginning, we prove the existence and uniqueness of the solution of nonlinear fuzzy Urysohn-Volterra delay integral equations (NFUVDIE). Then, we propose an iterative method and trapezoidal quadrature rule which numerically solve this equation. In addition, we prove the convergence analysis and error estimate of the proposed numerical method by theorem 3. Eventually, we conclude the efficiency of the presented method. Notice that the study of this equation is important since they have broad applications in various engineering sciences. Recently, a number of researchers suggested variant numerical methods for solving of Volterra fuzzy delay integral equations.