分数阶中立型随机时滞微分方程的波形松弛方法

Waveform relaxation method for fractional neutral stochastic delay differential equations

针对大多数分数阶中立型随机时滞微分方程无法给出精确解的问题,给出了方程的一种数值解法.该方法首先将波形松弛方法推广到具有常延迟项的分数阶中立型随机微分方程,然后在分裂函数满足Lipschliz条件下证明了波形松弛方法在均方意义下收敛.数值模拟表明,波形松弛方法可用于求解分数阶中立型随机时滞微分方程.

In order to solve the problem that most fractional neutral stochastic delay differential equations cannot give exact solutions,a numerical method is presented.The waveform relaxation method is extended to fractional neutral stochastic differential equations with constant delay terms,and then it is proved that the waveform relaxation method converges in the mean square sense under the Lipschliz condition of splitting function.Numerical simulation shows that the waveform relaxation method can be used to solve fractional neutral stochastic delay differential equations.