  In the present article, we discuss a numerical method of solution for the
so-called "full non-LTE" radiation transfer problem, basic formalism of which
was revisited by Paletou & Peymirat (2021; see also Oxenius 1986). More
specifically, usual numerical iterative methods for non-LTE radiation transfer
are coupled with the above-mentioned formalism. New numerical additions are
explained in detail. We benchmark the whole process with the standard non-LTE
transfer problem for a two-level atom with Hummer's (1962, 1969) $R_{\rm I-A}$
partial frequency redistribution function. We finally display new quantities
such as the spatial distribution of the velocity distribution function of
excited atoms, that can only be accessed to by adopting this more general frame
for non-LTE radiation transfer.
