Second Order Scheme for the Spatially Homogeneous Boltzmann Equation with Maxwellian Molecules

In the standard approach, particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction on the discretization parameter as well as on the diierential cross section in the case of the general Boltzmann equation. Recently, it was shown, how to construct an implicit particle scheme for the Boltzmann equation with Maxwellian molecules. The present paper combines both approaches using a linear combination of explicit and implicit discretizations. It is shown, that the new method leads to a second order particle method, when using an equiweighting of explicit and implicit discretization.