随机微分方程的Euler数值解法(英文)

Euler methods for numerical solution of stochastic ordinary differential equations

基于常微分方程(ODEs)的Euler数值解法,提出了求解一类随机常微分方程(SODEs)的3种Euler格式:显Euler格式,半隐Euler格式和隐Euler格式。讨论了3种Euler格式的T-稳定条件,并给出了部分数值实验结果。

Based on the well-established numerical methods for the deterministic ordinary differential equations the Euler method is applied to a scalar autonomous stochastic ordinary differential equation and three Euler numerical schemes are given： explicit scheme; semi-implicit sheme and implicit scheme. One type of stability of the Euler method, T-stability, is considered. Numerical results of a linear test equation show that the Euler method for solving SODEs is meaningful.