  Context. Type Ia supernovae (SN Ia) have become an invaluable cosmological
tool as their exceptional brightness makes them observable even at very large
distances (up to redshifts around z~1). To investigate possible systematic
differences between local and distant SN Ia requires detailed models whose
synthetic spectra can be compared to observations, and in which the solution of
the radiative transfer is a key ingredient. One commonly employed method is the
Feautrier scheme, which is generally very robust, but which can yield wrong
results under certain conditions that frequently occur in the modelling of
supernova ejecta or even in the radiatively driven expanding atmospheres of hot
stars.
  Methods. We use a sophisticated model atmosphere code which takes into
account the non-LTE effects and high velocity gradients that strongly affect
the physics of SN Ia atmospheres at all wavelengths to simulate the formation
of SN Ia spectra by the thousands of strong spectral lines which intricately
interact with the "pseudo-continuum" formed entirely by these Doppler-shifted
lines themselves. We focus to an investigation of the behavior of the Feautrier
scheme under these conditions.
  Results. Synthetic spectra of SN Ia, a complex product of computer models
replicating numerous physical processes that determine the conditions of matter
and radiation in the ejecta, are affected by large spatial jumps of the
line-dominated opacities and source functions for which the application of even
well-established methods may harbor certain pitfalls. We analyze the conditions
that can lead to a breakdown of conventional procedures and we derive for the
Feautrier radiative transfer solver a modified description which yields more
accurate results in the given circumstances.
