Numerical solution of two-dimensional nonlinear fuzzy delay integral equations via iterative method and trapezoidal quadrature rule

摘要

In recent years, fuzzy delay integral equation has received a considerable amount of attention. From the viewpoint of engineering, time delays in controllers may induce complex dynamic behavior and will limit the performance of the active control. Therefore, time delays play an important role in the dynamic behavior of active control systems. In our paper, we introduce an iterative method using trapezoidal quadrature formula for solving two-dimensional nonlinear fuzzy delay integral equations. In addition, the existence and uniqueness of the solution of these equations are proved. Also, the convergence analysis and a criterion to stop of the presented method are investigated. Moreover, we prove numerical stability analysis of the method through choosing the perturbation in the first iteration. Eventually, some numerical examples are provided to demonstrate the applicability of this procedure.