关键词: 随机微分方程, Euler方法, Milstein方法, 误差分析

Abstract: Stochastic differential equations are widely used in economy, biology, automation and other fields, but it is often difficult to find their closed solutions. In this paper, Euler method and Milstein method are applied to get the numerical solution of linear stochastic differential equation, and the numerical solutions are compared with closed solution. The accuracy of numerical methods, the relationship between error and step size are analyzed. The numerical results show that the Milstein method is more accurate than Euler method.

Key words: stochastic differential equations, Euler method, Milstein method, error analysis