A linear dispersive mechanism for numerical error growth: spurious caustics
Résumé
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.
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