  Our purpose is to evaluate the rate of the maximum energy and the
acceleration rate that cosmic rays acquire in the non-relativistic diffusive
shock acceleration as it could apply during their lifetime in various
astrophysical sites, where highly oblique shocks exist. We examine numerically
(using Monte Carlo simulations) the effect of the diffusion coefficients on the
energy gain and the acceleration rate, by testing the role between the
obliquity of the magnetic field to the shock normal, and the significance of
both perpendicular cross-field diffusion and parallel diffusion coefficients to
the acceleration rate. We find (and justify previous analytical work - Jokipii
1987) that in highly oblique shocks the smaller the perpendicular diffusion
gets compared to the parallel diffusion coefficient values, the greater the
energy gain of the cosmic rays to be obtained. An explanation of the cosmic ray
spectrum in high energies, between $10^{15}$eV and about $10^{18}$eV is
claimed, as we estimate the upper limit of energy that cosmic rays could gain
in plausible astrophysical regimes; interpreted by the scenario of cosmic rays
which are injected by three different kind of sources, (a) supernovae which
explode into the interstellar medium, (b) Red Supergiants, and (c) Wolf-Rayet
stars, where the two latter explode into their pre-supernovae winds.
