[en] Comparisons made by the Large Core Code Evaluation Working Group (LCCEWG) show that excellent agreement is obtained by different diffusion theory codes run on different computers at different installations in computing representative models of large fast reactors. It is noted that finite difference diffusion theory computer codes are still not fast enough to run the largest problems, but the coarse-mesh nodal expansion methods now seem capable not only of providing accurate global results in very short computing times, but also of recovering consistent local flux shapes. A new multigrid method due to Brandt gives promise of very effective acceleration of diffusion equation iterations and also makes possible adaptive mesh solution procedures. The latest version of the discrete ordinates code DOT-IV allows energy and spatial variation of the discrete ordinates quadrature order as well as a form of line deletion. The three-dimensional discrete ordinates code THREETRAN (hex,.z) has been successfully used to analyze problems representative of fast reactor systems during the approach-to-critical loading phase. New discrete ordinates difference schemes are described that include a more accurate, positive weighed diamond scheme, a positive geometric mean scheme, and the analog of the diamond scheme for triangular meshes