We developed a new computer code which is able to treat the time depen
dent photo-and collisional ionization of gaseous nebulae together with
the consistent energy balance for arbitrary numbers of elements, ions
and line transitions. The intention of this paper is to describe the
basic numerical methods and a few test calculations as being parts of
full spherically symmetric radiation-gasdynamic computations in the li
mit of a nonmoving gas (v(r) = 0). Exemplarily we discuss the evolutio
n of ionization fronts around a suddenly switched-on/switched-off cent
ral star with T-eff = 50 000 K and L = 6000 L.. Evidence is presented
that the photon velocities must artificially be limited in time depen
dent astrophysical calculations when the equation of radiative transfe
r is not explicitely treated in a time dependent way. Furthermore, com
putations with different spatial resolutions demonstrate that a carefu
l choice of the grid resolution in ionization calculations is essentia
l for the interpretation of observed line intensities.