Iterative numerical method for pantograph type fuzzy Volterra integral equations

Abstract

In this paper a sequence of fuzzy Bernstein spline interpolation procedure is considered for approximating the solution of pantograph type fuzzy Volterra integral equation. The numerical method is based on an iterative algorithm that applies at each iterative step the fuzzy Bernstein spline interpolation procedure and the Bernstein composite quadrature formula. The error estimate given in terms of the Lipschitz constants is used for obtaining the convergence of the iterative method. The theoretical results are tested on some numerical examples illustrating the accuracy of the method.