Numerical studies of hyperbolic IBVP with high-order finite difference operators satisfying a summation by parts rule

Abstract

Numerical studies on hyperbolic initial-boundary value problems (IBVP) have been performed using high-order difference operators satisfying a summation by parts rule. To assure that the numerical solution is strictly stable two recently developed methods by Carpenter et al. (1994) and Olsson (1995) to implement the analytic boundary conditions without destroying the summation by parts rule have been used. Theoretical and numerical results show that the numerical methods presented here are strictly stable and have a convergence rate that agrees well with the theory of Gustafsson (1975, 1981).