  We describe two separate wavelength discretization schemes that can be used
in the numerical solution of the comoving frame radiative transfer equation. We
present an improved second order discretization scheme and show that it leads
to significantly less numerical diffusion than previous scheme. We also show
that due to the nature of the second order term in some extreme cases it can
become numerically unstable. We stabilize the scheme by introducing a mixed
discretization scheme and present the results from several test calculations.
