On steady-state preserving spectral methods for homogeneous Boltzmann   equations
  In this note, we present a general way to construct spectral methods for the collision operator of the Boltzmann equation which preserves exactly the Maxwellian steady-state of the system. We show that the resulting method is able to approximate with spectral accuracy the solution uniformly in time. 
Francis Filbet and Lorenzo Pareschi and Thomas Rey
math.NA