UNCONDITIONALLY STABLE DIFFUSION-SYNTHETIC ACCELERATION METHODS FOR THE SLAB GEOMETRY DISCRETE ORDINATES EQUATIONS .1. THEORY

This paper considers the slab geometry discrete ordinates equations for neutron transport, with the weighted diamond, linear characteristic, linear discontinuous, and linear moments spatial differencing schemes. For each differencing scheme a diffusion-synthetic, source-correction acceleration method is derived which, for model (infinite medium, isotropic scattering, constant cross section, constant mesh spacing) problems, unconditionally reduces the spectral radius of the iteration method from the unaccelerated value of c (the scattering ratio) to less than c/3.