Mh. Carpenter et J. Otto, HIGH-ORDER CYCLE-DIFFERENCE TECHNIQUES - AN ALTERNATIVE TO FINITE-DIFFERENCES, Journal of computational physics, 118(2), 1995, pp. 242-260
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.