  We design numerical schemes for a class of slow-fast systems of stochastic
differential equations, where the fast component is an Ornstein-Uhlenbeck
process and the slow component is driven by a fractional Brownian motion with
Hurst index $H>1/2$. We establish the asymptotic preserving property of the
proposed scheme: when the time-scale parameter goes to $0$, a limiting scheme
which is consistent with the averaged equation is obtained. With this numerical
analysis point of view, we thus illustrate the recently proved averaging result
for the considered SDE systems and the main differences with the standard
Wiener case.
