A class of balanced stochastic Runge-Kutta methods for stiff SDE systems

Abstract

In this paper we present a family of balanced stochastic Runge-Kutta (BSRK) methods for stiff systems of stochastic differential equations (SDEs). This class of methods will have general framework for balancing the stochastic terms in arbitrary SRK methods of stochastic strong order p to get some balanced derivative-free methods of arbitrary stochastic order p. We also investigate the mean-square stability (MS-stability) properties for SDEs with stiffness in their drift and diffusion parts for some selected BSRK methods. Using such new methods, contrary to most existing derivative based balanced methods, in addition to having superior stability properties, one can get some significant reduction in computational cost. Numerical examples are presented to demonstrate the effectiveness of these methods for the pathwise approximation of solution of Ito SDEs.