  This paper is part of a program to combine a staggered time and staggered
spatial discretization of continuum wave equations so that important properties
of the continuum that are proved using vector calculus can be proven in an
analogous way for the discretized system. The spatial discretizations are
second order accurate and mimetic. The time discretizations second are order
accurate explicit leapfrog schemes. The discretizations have a conserved
quantity that guarantees stability for a reasonable constraint on the time
step. The conserved quantities are closely related to the energy for the
continuum equations.
