Numerical schemes are presented for dynamical systems with multiple
time-scales. Two classes of mehtods are discussed, depending on the
time interval which the evolution of the slow variables in the system
is sought. On rather short time intervals, the slow variables satisfy
ordinary differential equations. On longer time intervals, however,
fluctuations become important, and stochastic differential equations
are obtained. In both cases, the numerical methods compute the evolution
of the slow variables without having to derive explicitly the effective
equations beforehand; rather, the coefficients entering these equations are
obtained on the fly using simulations of appropriate auxiliary systems.