  Shock waves in molecular clouds should evolve into continuous or C-type
structures due to the magnetic field and ion-neutral friction. We here
determine whether and how this is achieved through plane-parallel numerical
simulations using an extended version of ZEUS. We first describe and test the
adapted code against analytical results, laying the necessary foundations for
subsequent works on supersonic ambipolar diffusion, including C-type jets and
shock instability.
  The evolution away from jump shocks toward the numerous steady C-shock
sub-types is then investigated. The evolution passes through four stages, which
possess distinctive observational properties. The time scales and length scales
cover broad ranges. Specific results are included for shock types including
switch, absorber, neutralised, oblique, transverse and intermediate. Only
intermediate Type II shocks and `slow shocks', including switch-off shocks,
remain as J-type under the low ion levels assumed. Other shocks transform via a
steadily growing neutral precursor to a diminishing jump. For neutralised
shocks, this takes the form of an extended long-lived ramp.
  Molecular hydrogen emission signatures are presented. After the jump speed
has dropped to under 25 km/s, a non-dissociative jump section can dominate the
spectra for a long period. This produces a high-excitation spectrum. Once the
jump has further weakened, to < 8 km/s, the fully developed ion front is
responsible for brisk progress towards a constant C-type excitation. The time
scale for emission-line variations is ~(6 /n_i) yr, where n_i is the pre-shock
ion number density.
