  We present a new many-parameter family of hyperbolic representations of
Einstein's equations, which we obtain by a straightforward generalization of
previously known systems. We solve the resulting evolution equations
numerically for a Schwarzschild black hole in three spatial dimensions, and
find that the stability of the simulation is strongly dependent on the form of
the equations (i.e. the choice of parameters of the hyperbolic system),
independent of the numerics. For an appropriate range of parameters we can
evolve a single 3D black hole to $t \simeq 600 M$ -- $1300 M$, and are
apparently limited by constraint-violating solutions of the evolution
equations. We expect that our method should result in comparable times for
evolutions of a binary black hole system.
