Convergence of a Weighted Particle Method for Solving the Boltzmann (B.G.K.) Equation

We consider in this paper the numerical solution of the B.G. K. model for the Boltzmann equation. The numerical method used here was introduced by Mas-Gallic (Transport Theory Statist. Phys., 16 (1987), pp. 885--887). Using the results of Perthame and Pulvirenti (Arch. Rational Mech. Anal., 125 (1993), pp. 289--295) we first derive a uniqueness result for the B.G. K. model and also regularity properties of the solution which are necessary for our analysis. We then prove, following Mas-Gallic and Poupaud (Transport Theory Statist. Phys., 17 (1988), pp. 311--345), the convergence of the numerical approximation for the B.G. K. model. Finally, some numerical experiments are presented.