Analysis and comparison of two approximation schemes for a radiative transfer system

This paper analyzes two algorithms based on the S-2 approximation for the evolutive, gray, 1D radiative transfer equations in the slab with isotropic scattering. It is known that simple fixed point iteration does not work when the medium is optically thick, and that this difficulty can be overcome by using a Newton method. In this paper we quantify the first observation, giving a criterium to decide a priori whether fixed point converges or not. We also observe that the Newton method can be implemented faster than the fixed point iteration, but this implementation strongly relies on the particular discretization schemes used here. Existence theorems for the discrete nonlinear problem axe also proved.