An application of a semi-analytical method on linear fuzzy Volterra integral equations

Abstract

Recently, fuzzy integral equations have attracted some interest. In this paper, we focus on linear fuzzy Volterra integral equation of the second kind (FVIE-2) and propose a new method for numerical solving it. In fact, using parametric form of fuzzy numbers we convert a linear fuzzy Volterra integral equation of the second kind to a linear system of Volterra integral equations of the second kind in crisp case. We use variational iteration method (VIM) and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy Volterra integral equation of the second kind. Finally, using the proposed method, we give some illustrative examples.