  We study a model problem describing vibrational resonance by means of a
high-order averaging technique based on so-called word series. With the tech-
nique applied here, the tasks of constructing the averaged system and the
associ- ated change of variables are divided into two parts. It is first
necessary to build recursively a set of so-called word basis functions and,
after that, all the required manipulations involve only scalar coefficients
that are computed by means of sim- ple recursions. As distinct from the
situation with other approaches, with word- series, high-order averaged systems
may be derived without having to compute the associated change of variables. In
the system considered here, the construction of high-order averaged systems
makes it possible to obtain very precise approxima- tions to the true dynamics.
