半线性随机变延迟微分方程数值解的收敛性

摘要

The authors used the exponential Euler method to make the numerical solution convergence for semi-linear stochastic variable delay differential equation under the global Lipschitz condition and the linear growth condition, and the numerical solutions converge to the exact solution. The convergence order is 12 min{1,γ},γ∈(0,1].%应用指数Euler方法研究在全局Lipschitz条件和线性增长条件下,半线性随机变延迟微分方程数值解的收敛性。结果表明,该方程数值解收敛到精确解,并且收敛阶为12 min{1,γ},γ∈(0,1]。