  We present a general formalism for computing self-consistent, numerical
solutions to the time-dependent radiative transfer equation in low velocity,
multi-level ions undergoing radiative interactions. Recent studies of
time-dependent radiative transfer have focused on radiation hydrodynamic and
magnetohydrodynamic effects without lines, or have solved time-independent
equations for the radiation field simultaneously with time-dependent equations
for the state of the medium. In this paper, we provide a fully time-dependent
numerical solution to the radiative transfer and atomic rate equations for a
medium irradiated by an external source of photons. We use Accelerated Lambda
Iteration to achieve convergence of the radiation field and atomic states. We
perform calculations for a three-level atomic model that illustrates important
time-dependent effects. We demonstrate that our method provides an efficient,
accurate solution to the time-dependent radiative transfer problem. Finally, we
characterize astrophysical scenarios in which we expect our solutions to be
important.
