Collocation method for fuzzy Volterra integral equations of the second kind

Abstract

In this paper we consider fuzzy Volterra integral equation of the second kind whose kernel may change sign. We give conditions for smoothness of the upper and lower functions of the solution. For numerical solution we propose the collocation method with two different basis function sets: triangular and rectangular basis. The smoothness results allow us to obtain the convergence rates of the methods. The proposed methods are illustrated by numerical examples, which confirm the theoretical convergence estimates.

Keywords

• fuzzy Volterra integral equation
• smoothness of solution
• triangular basis
• rectangular basis
• collocation method
• convergence rate