  The development of accurate and fast numerical schemes for the five fold
Boltzmann collision integral represents a challenging problem in scientific
computing. For a particular class of interactions, including the so-called hard
spheres model in dimension three, we are able to derive spectral methods that
can be evaluated through fast algorithms. These algorithms are based on a
suitable representation and approximation of the collision operator. Explicit
expressions for the errors in the schemes are given and spectral accuracy is
proved. Parallelization properties and adaptivity of the algorithms are also
discussed.
