Boundary Conditions for Hyperbolic Systems of Partial Differential Equations Having Multiple Time Scales

摘要

This paper is concerned with linear hyperbolic systems of partial differential equations for which certain of the associated propagation speeds are a great deal larger than the other propagation speeds. In certain cases the fast modes allowed by such a system are not present in the true physical solution. Yet the fact that such modes are allowed means that when one tries to compute a numerical solution to an initial-boundary value problem, the errors generated can propagate quite rapidly. In particular, when the boundary data used for the computation are less accurate then the initial data, the fast modes can cause a rapid contamination of the calculation in the interior. To prevent this, one would like to have boundary conditions which prevent fast waves from entering the region. The goal of this paper is to find such conditions.