随机微分方程2种数值方法的稳定性分析

给出了求解随机微分方程的2种数值方法:有限差分法和向后Milstein法,基于随机微分方程的试验方程分析讨论了2种数值方法的均方稳定性和A-稳定性,得到了相应的稳定性条件和稳定域.最后应用MatLab进行模拟演示,模拟演示结果表明,有限差分法和向后Milstein法都全局一阶强收敛于随机微分方程的求解过程,并且验证了均方稳定理论的正确性.

Stability Analysis of Two Numerical Schemes for Stochastic Differential Equations

A backward Milstein scheme and a finite difference scheme are provided for stochastic differential equations.The stability of the two numerical schemes:the mean-square stability,A-stability,is studied on the basis of the two types of test equations of stochastic differential equations.The corresponding conditions for stability and stability regions are obtained.At last,simulations using the two numerical schemes are operated in MatLab,which illustrate that a backward Milstein scheme and a finite difference scheme both convergence with strong order 1 and testify the theory of mean-square stability.