On the Convergence of Finite-Differenced Multigroup, Discrete-Ordinates Methods for Anisotropically Scattered Slab Media

Abstract

A convergence analysis is provided for the multigroup, discrete-ordinates method used to numerically solve the linear transport equation for anisotropically scattering, subcritical slab media. Characteristic finite-difference methods for discretizing the spatial variable are considered. The multigroup fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution to the linear transport equation. This is the first thorough convergence analysis for the fully discretized multigroup slab transport equations.