  A linear dispersive mechanism leading to a burst in the $L_\infty$ norm of
the error in numerical simulation of polychromatic solutions is identified.
This local error pile-up corresponds to the existence of spurious caustics,
which are allowed by the dispersive nature of the numerical error. From the
mathematical point of view, spurious caustics are related to extrema of the
numerical group velocity and are physically associated to interactions between
rays defined by the characteristic lines of the discrete system. This paper
extends our previous work about classical schemes to dispersion-relation
preserving schemes.
