An Infinite Family of Second Order Weak Explicit Runge-Kutta Methods

Abstract

A quick overview of the fundamental concepts for the construction of weak methods for the numerical solution of stochastic differential equations and a new way to construct these methods are presented. As in the deterministic case, the presented procedure to obtain these methods consists in the comparison of their stochastic expansions with the corresponding Taylor scheme. In this way the authors construct a generalization of the classical second order two step explicit Runge-Kutta family of methods for ordinary differential equations. The obtained methods require the computation of a random variable at each step and avoid derivatives.