HIGH-ORDER CYCLE-DIFFERENCE TECHNIQUES - AN ALTERNATIVE TO FINITE-DIFFERENCES

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as ''cycle-d ifference'' techniques. These techniques are constructed cyclically fr om 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 implementa tion, but they do not require special collocation points. The principa l focus of th is work is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arb itrary order of accuracy. (c) 1995 Academic Press, Inc.