New S-ROCK methods for stochastic differential equations with commutative noise

Abstract

The class of strong stochastic Runge–Kutta (SRK) methods for stochas tic differential equations with a commutative noise proposed by R¨ oßler (2010) is considered. Motivated by Komori and Burrage (2013), we design a class of explicit stochastic orthogonal Runge–Kutta Chebyshev (SROCKC2) meth ods of strong order one for the approximation of the solution of Itˆo SDEs with an m-dimensional commutative noise.The mean-square and asymptotic stability analysis of the newly proposed methods applied to a scalar linear test equation with a multiplicative noise is presented. Finally, some numer ical experiments for stochastic models arising in applications are given that confirm the theoretical discussion.

Keywords

• stochastic differential equations
• runge-kutta methods
• stochastic mean square stability
• stiff equations
• commutative noise