  A linear dispersive mechanism for error focusing in 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. Several popular schemes are analyzed
and are shown to admit spurious caustics. It is also observed that caustic-free
schemes can be defined, like the Crank-Nicolson scheme.
