  The second Bianchi identity can be recast as an evolution equation for the
Riemann curvatures. Here we will report on such a system for a vacuum static
spherically symmetric spacetime. This is the first of two papers. In the
following paper we will extend the ideas developed here to general vacuum
spacetimes. In this paper we will demonstrate our ideas on a Schwarzschild
spacetime and give detailed numerical results. For suitable choices of lapse
function we find that the system gives excellent results with long term
stability.
