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An asymptotic preserving numerical scheme (with respect to diffusion scalings) for a linear transport equation is investigated. The scheme is adopted from a class of schemes developed in S. Jin, L. Pareschi, and G. Toscani, SIAM J. Numer. Anal., 38 (2000), pp. 913--936 and A. Klar, SIAM J. Numer. Anal., 35 (1998), pp. 1073--1094. Stability is proven uniformly in the mean free path under a CFL-type condition turning into a parabolic CFL condition in the diffusion limit.
Klar et al. (Tue,) studied this question.
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