It is shown that the use of the standard spatial-differencing method when applied to space-time diffusion problems arising as the materials within a reactor are displaced can result in solutions which display a nonphysical time dependence. This irregular time dependence occurs when the spatial mesh and timestep are such that it takes several time steps for a movable material interface to move between two spatial meshpoints. New spatial difference equations, based on a specified piecewise polynomial flux behavior between meshpoints, are developed for the space-time group diffusion equations. Numerical studies show that these new difference equations eliminate the nonphysical time dependence of the solution for movable material problems. In addition, it is shown that for such problems the solutions resulting from the new difference equations are almost as accurate as solutions obtained using the standard difference equations with a much finer spatial mesh.