Explicit Order 1.5 Schemes for the Strong Approximation of Itô Stochastic Differential Equations

Abstract

A new class of stochastic Runge‐Kutta (SRK) methods for the strong approximation of It ô stochastic differential equation systems w.r.t. an one‐dimensionalWiener process is introduced. Some coefficients for a SRK method converging at least with order 1.5 in the strong sense are presented. Further, a special SRK scheme having deterministic order 4.0 is proposed for stochastic differential equations with small noise. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)