Galerkin-Petrov approach for the Boltzmann equation

In this work, we propose a new Galerkin-Petrov method for the numerical solution of the classical spatially homogeneous Boltzmann equation. This method is based on an approximation of the distribution function by associated Laguerre polynomials and spherical harmonics and test in a variational manner with globally defined three-dimensional polynomials. A numerical realisation of the algorithm is presented. The algorithmic developments are illustrated with the help of several numerical tests.