  Many numerical codes now under development to solve Einstein's equations of
general relativity in 3+1 dimensional spacetimes employ the standard ADM form
of the field equations. This form involves evolution equations for the raw
spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura,
we modify these equations by factoring out the conformal factor and introducing
three ``connection functions''. The evolution equations can then be reduced to
wave equations for the conformal metric components, which are coupled to
evolution equations for the connection functions. We evolve small amplitude
gravitational waves and make a direct comparison of the numerical performance
of the modified equations with the standard ADM equations. We find that the
modified form exhibits much improved stability.
