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

摘要

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.