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In this paper we give an introduction to the Boltzmann equation for neutrinotransport used in core collapse supernova models as well as a detailedmathematical description of the \emph{Isotropic Diffusion Source Approximation}(IDSA). Furthermore, we present a numerical treatment of a reduced Boltzmannmodel problem based on time splitting and finite volumes and revise thediscretization of the IDSA for this problem. Discretization error studiescarried out on the reduced Boltzmann model problem and on the IDSA show thatthe errors are of order one in both cases. By a numerical example, a detailedcomparison of the reduced model and the IDSA is carried out and interpreted.For this example the IDSA modeling error with respect to the reduced Boltzmannmodel is numerically determined and localized.

A Mathematical Description of the IDSA for Supernova Neutrino transport,  its discretization and a comparison with a finite volume scheme for  Boltzmann's Equation