  We present a study of numerical effects in dissipationless cosmological
simulations. The numerical effects are evaluated and studied by comparing
results of a series of 64^3-particle simulations of varying force resolution
and number of time steps, performed using three different N-body techniques:
the Particle Mesh (PM), the adaptive P3M (AP3M) code, and the Adaptive
Refinement Tree (ART) code. This study can therefore be interesting both as an
analysis of numerical effects and as a systematic comparison of different
codes. We find that the AP3M and the ART codes produce similar results, given
that convergence is reached within the code type. We also find that numerical
effects may affect the high-resolution simulations in ways that have not been
discussed before. In particular, our study revealed the presence of two-body
scattering, effects of which can be greatly amplified by inaccuracies of time
integration. This process appears to affect the correlation function of matter,
mass function and inner density of dark matter halos and other statistics at
scales much larger than the force resolution, although different statistics may
be affected in different fashion. We discuss the conditions at which strong
two-body scattering is possible and discuss the choice of the force resolution
and integration time step. Furthermore, we discuss recent claims that
simulations with force softening smaller than the mean interparticle separation
are not trustworthy and argue that this claim is incorrect in general and
applies only to the phase-sensitive statistics. Our conclusion is that,
depending on the choice of mass and force resolution and integration time step,
a force resolution as small as 0.01 of the mean interparticle separation can be
justified.
