  We propose a new numerical scheme of evolution for the Einstein equations
using the discrete variational derivative method (DVDM). We derive the discrete
evolution equation of the constraint using this scheme and show the constraint
preserves in the discrete level. In addition, to confirm the numerical
stability using this scheme, we perform some numerical simulations by
discretized equations with the Crank-Nicolson scheme and with the new scheme,
and we find that the new discretized equations have better stability than that
of the Crank-Nicolson scheme.
