  Context. Solar energetic particles observed in association with coronal mass
ejections (CMEs) are produced by the CME-driven shock waves. The acceleration
of particles is considered to be due to diffusive shock acceleration (DSA).
Aims. We aim at a better understanding of DSA in the case of quasi-parallel
shocks, in which self-generated turbulence in the shock vicinity plays a key
role. Methods. We have developed and applied a new Monte Carlo simulation code
for acceleration of protons in parallel coronal shocks. The code performs a
self-consistent calculation of resonant interactions of particles with Alfv\'en
waves based on the quasi-linear theory. In contrast to the existing Monte Carlo
codes of DSA, the new code features the full quasi-linear resonance condition
of particle pitch-angle scattering. This allows us to take anisotropy of
particle pitch-angle scattering into account, while the older codes implement
an approximate resonance condition leading to isotropic scattering.We performed
simulations with the new code and with an old code, applying the same initial
and boundary conditions, and have compared the results provided by both codes
with each other, and with the predictions of the steady-state theory. Results.
We have found that anisotropic pitch-angle scattering leads to less efficient
acceleration of particles than isotropic. However, extrapolations to particle
injection rates higher than those we were able to use suggest the capability of
DSA to produce relativistic particles. The particle and wave distributions in
the foreshock as well as their time evolution, provided by our new simulation
code, are significantly different from the previous results and from the
steady-state theory. Specifically, the mean free path in the simulations with
the new code is increasing with energy, in contrast to the theoretical result.
