Time-dependent processes of solid propellant deflagration are modeled and a numerical simulation of ignition and extinction is undertaken. Since the analytic theory of ignition is well developed we rely on it to verify the ability of the numerical algorithm to track stiff, time-dependent features of an ignition event. The verification of our numerical method provides a degree of confidence for the subsequent study of deradiation, which is less well understood. An activation energy asymptotic theory for deradiation is developed, which predicts that an influx of radiation on the order of the steady heat release of the exothermic reaction will, at near term, extinguish the propellant. Beyond this, conduction processes inherited from the thermal profile at the instant of deradiation may, or may not, cause resumption of pyrolysis, and, presumably, the deflagration as a whole. The analytic theory ignores the subsequent impact of a possible gas-phase flame that is detached many conductive--diffusive lengths away from the gas/solid surface. The assumption is based on the observation that for most physical systems the gas density--and hence its thermal capacitance--is many times smaller than that of the solid and thus lacks the potential to alter the surface temperature after deradiation. The simulation is used to verify more complicated and more physical situations than those accessible via the theory, including deradiation with a detached flame and in the presence of an instability.