Numerical methods for the generation of the spectrum of the multigroup slab-geometry discrete ordinates operator in neutron transport theory

We describe two numerical methods applied to the first-order form of the multigroup slab-geometry discrete ordinates equations modelling fixed-source neutron transport problems with anisotropic scattering. The numerical methods described in this article generate the spectrum and a vector basis for the null space of the multigroup slab-geometry discrete ordinates operator defined in a homogeneous domain. The first method is a more general approach of a numerical method described in a recent work by others. We then come to consider numerical and computational aspects of the first method and we propose a second method. The second method is a multigroup extension of a numerical method described in a more recent work by the present author. In order to provide those interested in implementing either method with a reference set, we present numerical results for some multigroup slab-geometry model problems with anisotropic scattering. We conclude this article with a discussion and directions for future work.