Collocation Method for Fuzzy Volterra Integral Equation of the Second Kind with Weakly Singular Kernels

Abstract

In this paper we consider fuzzy Volterra integral equation of the second kind with weakly singular kernel. We propose piecewise spline collocation methods with a graded mesh. By increasing the number of collocation points we show that the numerical solution exists and converges to the exact solution. We obtain exact convergence vlues depending on smoothness of the solution and on the grading parameter of the mesh.We give sufficient conditions for the fuzziness of the approximate solution. The proposed method is illustrated by numerical examples which confirm the theoretical convergence estimates.