and

The stability theory for finite difference Initial Boundary-Value approximations to sys-tems of hyperbolic partial differential equations states that the exclusion 8ieigenvalues!.nd generalized eigenvalues is a sufficient condition for stability. The theory, ho e er, does not discuss the nature of numerical apprvimations in the presence of such eigenval es. In fact, as was shown previously4M, for the problem of vortex shedding by a 2- cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. In this paper, we report on a more systematic study of the behavior of the (linearized)$ one-dimensional gas dynamic equations under various sets of oscillation-inducing f'legal \ boundary conditions