A collocation technique for solving nonlinear Stochastic Itô-Volterra integral equations

A numerical method for solving nonlinear Stochastic Itô-Volterra equations is proposed. The method is based on delta function (DF) approximations. The properties of DFs and their operational matrix of integration together with the Newton-Cotes nodes are presented and utilized to reduce the problem to the solution of a nonlinear system of algebraic equations. The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.