Numerical studies of hyperbolic IBVP with high-order finite difference operators satisfying a summation by parts rule
Numerical studies of hyperbolic initial-boundary value problems (IBVPs) are presented using high-order difference operators satisfying a summation by parts rule. Two recently developed methods by \textit{M. H. Carpenter} et al. [J. Comput. Phys. 111, No. 2, 220--236 (1994; Zbl 0832.65098)] and by \textit{P. Olsson} [Math. Comput 64, No. 211, 1035--1065, Supplement S23--S26 (1995; Zbl 0828.65111); ibid. 64, No. 212, 1473--1493 (1995; Zbl 0848.65064)] are used. The numerical methods are strictly stable and have a convergence rate that agrees well with the theory of \textit{B. Gustafsson} [SIAM J. Numer. Anal. 18, 179--190 (1981; Zbl 0469.65068)].
hyperbolic initial-boundary value problems
scientific article; zbMATH DE number 1311230