非线性随机延迟微分方程θ-Heun方法的稳定性

Stability of θ-Heun methods for nonlinear stochastic delay differential equations

提出了求解随机延迟微分方程的θ-Heun方法。对于一般非线性随机延迟微分方程,得到了θ-Heun方法MS-稳定,GMS-稳定和均方指数稳定的充分条件,与Heun方法相比,θ-Heun方法对于步长的限制更小。文末的数值试验验证了相关结论。

The θ-Heun method for solving stochastic delay differential equations is presented.Based on this method,sufficient conditions for general nonlinear stochastic delay differentials equations are obtained for the MS-stability,GMS-stability and exponential stability of mean square.Compared with the Heun method,the θ-Heun method has less restriction on step size.The numerical experiments at the end of the paper verify the relevant conclusions.