线性随机比例延迟微分方程的半隐式Euler方法的均方稳定性

Stability of the semi-implicit euler method for a linear stochastic pantograph delay differential equation

定义了变步长半隐式Enler方法,并将其应用于线性随机比例延迟微分方程,得到方程数值方法的差分方程,并证明了在随机比例延迟微分方程解析解均方稳定的条件下,当半隐式Euler方法中的参数θ满足条件θ∈((|a|+|b|)/(2|a|),1]时,此方法应用于线性随机比例延迟微分方程所得的数值解是均方稳定的。最后给出了数值算例。

The semi -implicit Euler method with rariable stepsize is defined and used to solve the stochastic pantograph delay differential equation. It is shown that under the condition of stability of exact solution the semi - implict Euler method with rariable stepsize is stabe if θ∈（｜a｜＋｜b｜/2｜a｜,1].In the last section,the numerical examples are gaven.