Improved rectangular method on stochastic Volterra equations

摘要

An improved version of rectangular method (IRM) is introduced in this paper to numerically solve the stochastic Volterra equation (SVE). We focus on studying the order of error between the numerical and exact solutions, which is improved to O(h). Furthermore, an explicit form of the IRM scheme is introduced and its convergence is established. A numerical example has also been presented to show the feasibility of the methods.