Abstract: According to colored rooted tree theory, this paper presents two classes of three-stage semi-implicit stochastic Runge-Kutta methods for solving Stratonovich type stochastic differential equations, and analyzes their mean square stability. The stable regions of these methods are larger than those of the extant methods. The numerical simulation results show the high accuracy of the methods in this paper.

Key words: stochastic differential equations, colored rooted tree, three-stage stochastic Runge-Kutta method, mean square stability

摘要： 根据彩色树理论，构造了两种求解Stratonovich型随机微分方程的半隐式三阶随机Runge-Kutta方法，给出了这两种方法的稳定性分析，其稳定区域比现有方法的稳定区域大；数值模拟的结果表明两个方法都具有较高的精度。

关键词: 随机微分方程, 彩色树, 三阶随机Runge-Kutta方法, 均方稳定