  This is the first in a series of papers on the effects of dust on the
formation, propagation, and structure of nonlinear MHD waves and MHD shocks in
weakly-ionized plasmas. We model the plasma as a system of 9 interacting
fluids, consisting of the neutral gas, ions, electrons, and 6 grain fluids
comprised of very small grains or PAHs and classical grains in different charge
states. We formulate the governing equations for perpendicular shocks under
approximations appropriate for dense molecular clouds, protostellar cores, and
protoplanetary disks. We describe a code that obtains numerical solutions using
a finite difference method, and estabish its accuracy by comparing numerical
and exact solutions for special cases.
