The design and safety analysis of the next generation of advanced nuclear reactors will require the use high-fidelity multiphysics simulations. To that effect a novel multidimensional radiation transport method is being developed based on the slice balance approach. This class of method is a variant of the well-established discrete ordinates method and is very well suited for unstructured computational grids. In this thesis a time-dependent framework will be developed in order to address transient problems. This framework will be general in that it will take into account both prompt and delayed neutrons, and will allow the choice of main time-integrating schemes. The effectiveness of these schemes will be analyzed with respect to the discretization of each phase-space variable in the transport equation.