A. Bobylev and S. Rjasanow, Fast deterministic method of solving the Boltzmann equation for hard spheres, European Journal of Mechanics - B/Fluids, vol.18, issue.5, pp.869-887, 1999.
DOI : 10.1016/S0997-7546(99)00121-1

A. Bobylev, Exact solutions of the Boltzmann equation, Dokl. Akad. Nauk SSSR, vol.225, pp.1296-1299, 1975.

C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, 1994.
DOI : 10.1007/978-1-4419-8524-8

F. Filbet and C. Mouhot, Analysis of spectral methods for the homogeneous Boltzmann equation, Transactions of the American Mathematical Society, vol.363, issue.04, pp.1947-1980, 2011.
DOI : 10.1090/S0002-9947-2010-05303-6
URL : https://hal.archives-ouvertes.fr/hal-00659629

F. Filbet, C. Mouhot, and L. Pareschi, Solving the Boltzmann Equation in N log2 N', SIAM, J. Sci. Comput, vol.28, issue.3, pp.1029-1053, 2007.

I. Gamba and S. Tharkabhushanam, Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states, Journal of Computational Physics, vol.228, issue.6, pp.2012-2036, 2009.
DOI : 10.1016/j.jcp.2008.09.033

D. Gottlieb and S. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM CBMS- NSF Series, 1977.
DOI : 10.1137/1.9781611970425

J. Greenberg and A. Leroux, A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996.
DOI : 10.1137/0733001

M. Krook and T. Wu, Exact solutions of the Boltzmann equation, Physics of Fluids, vol.20, issue.10, pp.1589-1595, 1977.
DOI : 10.1063/1.861780

C. Mouhot and L. Pareschi, Fast methods for the Boltzmann collision integral, Comptes Rendus Mathematique, vol.339, issue.1, pp.71-76, 2004.
DOI : 10.1016/j.crma.2004.04.010

M. Lemou, Relaxed micro???macro schemes for kinetic equations, Comptes Rendus Mathematique, vol.348, issue.7-8, pp.455-460, 2010.
DOI : 10.1016/j.crma.2010.02.017
URL : https://hal.archives-ouvertes.fr/hal-00521523

T. Liu and S. Yu, Boltzmann Equation: Micro-Macro Decompositions and Positivity of Shock Profiles, Communications in Mathematical Physics, vol.246, issue.1, pp.133-179, 2004.
DOI : 10.1007/s00220-003-1030-2

L. Pareschi and B. Perthame, A Fourier spectral method for homogeneous boltzmann equations, Transport Theory and Statistical Physics, vol.52, issue.3-5, pp.369-383, 1996.
DOI : 10.1103/PhysRevLett.36.1107

L. Pareschi and G. Russo, Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1217-1245, 2000.
DOI : 10.1137/S0036142998343300

F. Filbet, C. Université-de-lyon, and . Umr, F-69622 Villeurbanne cedex, France. E-mail address: filbet@math.univ-lyon1, Italy E-mail address: lorenzo.pareschi@unife.it Thomas Rey, Center of Scientific Computation and Mathematical Modeling (CSCAMM), pp.20742-4015, 1918.