In this section we present a test of the terms and finite difference representations introduced since Mezzacappa_Bruenn_93a. First, we investigate the diffusion limit in our finite difference representation and demonstrate that a small diffusive flux is accurate in the presence of a large, nearly isotropic radiation field. We also check the other extreme, the evolution of the radiation moments in a free streaming situation in spherically symmetric geometry. Another test in stationary space-time investigates the implementation of gravitational terms, such as number luminosity conservation, gravitational frequency shift, and gravitational bending. The frequency shift and angular aberration of the radiation field are probed at the shock front, where we relate the discontinuity in radiation quantities in the comoving frame to the smooth radiation field in the view of stationary observers. Then, we investigate the resolution dependence of our results and perform a detailed energy and lepton number conservation analysis to check the overall consistency of our code. Finally, in the intended application of stellar core collapse and postbounce evolution, we compare our results with the independently developed multi-group flux-limited diffusion (MGFLD) code of Bruenn_DeNisco_Mezzacappa_01. The latter is based on a sophisticated but approximative treatment of radiative transfer in spherical symmetry and uses a different hydrodynamics code.