  We show that a reformulation of the ADM equations in general relativity,
which has dramatically improved the stability properties of numerical
implementations, has a direct analogue in classical electrodynamics. We
numerically integrate both the original and the revised versions of Maxwell's
equations, and show that their distinct numerical behavior reflects the
properties found in linearized general relativity. Our results shed further
light on the stability properties of general relativity, illustrate them in a
very transparent context, and may provide a useful framework for further
improvement of numerical schemes.
