  We develop a powerful numerical algorithm for calculating the density of
states rho(omega) of the fluctuating gap model, which describes the low-energy
physics of disordered Peierls and spin-Peierls chains. We obtain rho(omega)
with unprecedented accuracy from the solution of a simple initial value problem
for a single Riccati equation. Generating Gaussian disorder with large
correlation length xi by means of a simple Markov process, we present a
quantitative study of the behavior of rho (omega) in the pseudogap regime. In
particular, we show that in the commensurate case and in the absence of forward
scattering the pseudogap is overshadowed by a Dyson singularity below a certain
energy scale omega^{ast}, which we explicitly calculate as a function of xi.
