  We introduce a new code for computing time-dependent continuum radiative
transfer and non-equilibrium ionization states in static density fields with
periodic boundaries. Our code solves the moments of the radiative transfer
equation, closed by an Eddingtion tensor computed using a long characteristics
method. We show that pure (i.e., not source-centered) short characteristics and
the optically-thin approximation are inappropriate for computing Eddington
factors for the problem of cosmological reionization. We evolve the
non-equilibrium ionization field via an efficient and accurate (errors <1%)
technique that switches between fully implicit or explicit finite-differencing
depending on whether the local timescales are long or short compared to the
timestep. We tailor our code for the problem of cosmological reionization. In
tests, the code conserves photons, accurately treats cosmological effects, and
reproduces analytic Stromgren sphere solutions. Its chief weakness is that the
computation time for the long characteristics calculation scales relatively
poorly compared to other techniques (t_{LC} \propto N_{cells}^1.5); however, we
mitigate this by only recomputing the Eddington tensor when the radiation field
changes substantially. Our technique makes almost no physical approximations,
so it provides a way to benchmark faster but more approximate techniques. It
can readily be extended to evolve multiple frequencies, though we do not do so
here. Finally, we note that our method is generally applicable to any problem
involving the transfer of continuum radiation through a periodic volume.
