A general finite difference discretization of the time-dependent radiation transport equation is developed around the framework of an existing steady-state three dimensional radiation transport solver based on the slice-balance approach. Three related algorithms are outlined within the general finite difference scheme: an explicit, an implicit, and a semi-implicit approach. The three algorithms are analyzed with respect to the discretizations of each element of the phase space in the transport solver. The explicit method, despite its small computational cost per time step, is found to be unsuitable for many purposes due to its inability to accurately handle rapidly varying solutions. The semi-implicit method is shown to produce results nearly as reliable as the fully implicit solver, while requiring significantly less computational effort.