We analyze the excision strategy for simulating black holes. The problem is
modeled by the propagation of quasi-linear waves in a 1-dimensional spatial
region with timelike outer boundary, spacelike inner boundary and a horizon in
between. Proofs of well-posed evolution and boundary algorithms for a second
differential order treatment of the system are given for the separate pieces
underlying the finite difference problem. These are implemented in a numerical
code which gives accurate long term simulations of the quasi-linear excision
problem. Excitation of long wavelength exponential modes, which are latent in
the problem, are suppressed using conservation laws for the discretized system.
The techniques are designed to apply directly to recent codes for the Einstein
equations based upon the harmonic formulation.Comment: 21 pages, 14 postscript figures, minor contents updat