2ND-ORDER SCHEME FOR THE SPATIALLY HOMOGENEOUS BOLTZMANN-EQUATION WITH MAXWELLIAN MOLECULES

In the standard approach particle methods for the Boltzmann equation a re obtained using an explicit time discretization of the spatially hom ogeneous Boltzmann equation. This kind of discretization leads to a re striction on the discretization parameter as well as on the differenti al cross-section in the case of the general Boltzmann equation. Recent ly, construction of an implicit particle scheme for the Boltzmann equa tion with Maxwellian molecules was shown. This paper combines both app roaches using a linear combination of explicit and implicit discretiza tions. It is shown that the new method leads to a second-order particl e method when using an equiweighting of explicit and implicit discreti zation.