Some drift exponentially fitted stochastic Runge-Kutta methods for solving It\^{o} SDE systems

Abstract

In this paper, we introduce a family of drift exponentially fitted stochastic Runge-Kutta (DEFSRK) methods for multi-dimensional It\^{o} stochastic differential equations (SDEs). For the presented class of DEFSRK methods, the regions of mean-square stability (MS-stability) are obtained with reasonable results. Also, general order conditions for the coefficients and the random variables of the DEFSRK methods are extracted. Then, a set of order conditions for a subclass with stochastic weak second order is obtained. Some numerical examples are presented to establish the efficiency and accuracy of the new schemes.