Abstract
The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as "cyclo-difference" techniques. These techniques are constructed cyclically from stable subelements and require no special numerical procedures near the boundaries; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral multi-domain techniques and are ideally suited for parallel implementation, but they do not require special collocation points. The principal focus of this work is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.
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