Numerical solution of stochastic Itô-Volterra integral equations by Legendre spectral collocation method

The purpose of this paper is to propose the spectral collocation method to solve linear and nonlinear stochastic Itô-Volterra integral equations (SVIEs). The proposed approach is different from existing numerical techniques as we consider the Legendre Gauss type quadrature for estimating Itô integrals. The main characteristic of the presented method is that it reduces SVIEs into a system of algebraic equations. Finally, numerical examples show the efficiency of the proposed method