Detonation Shock Dynamics (DSD) is an important tool to model the behavior of detonations in High Explosives (HE). By evolving the location of the detonation front rather than solving for it through the direct solution of the unsteady reactive Euler equations, simulations can be run at significantly larger spatial and temporal resolutions, with little loss in accuracy. However, the accuracy of the DSD solution depends on the underlying model of how the local velocity of the detonation front changes with its current state. The original DSD theory proposed the that the local detonation speed was a function of local curvature alone, future work extended add the effects the first derivative of the detonation speed with respect to time and the second derivative of the detonation speed with respect to the arc length along the detonation front. Previous work has sought to identify these DSD models, though they have often focused on polytropic equation of state models and Arrhenius kinetics. Recent work has investigated using newer and more complex models for both equation of state and reaction rates to identify the underlying DSD relationship implied by recently developed burn models such as AWSD. The present verification exercise will extend the governing equations from the steady curved detonation wave to a detonation accelerating at a constant, known, rate. These new governing equations will be verified against known exact solutions and high accuracy interrogations for the case of planar detonation and against existing asymptotic solutions for the case of a curved, accelerating detonation wave.