随机微分方程的数值求解

Numerical Solution of Stochastic Differential Equations

随机微分方程广泛应用于经济,生物和自动化等领域,通常难以求出其解析解.利用Euler方法和Milstein方法分别给出线性随机微分方程的数值解,将数值解与解析解进行比较,给出两种方法的精度,分析说明步长和误差的关系.数值实验结果表明Milstein方法得出的数值解比Euler方法更精确.

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.