  The joint influence of numerical parameters such as the number of particles
N, the gravitational softening length $\epsilon$ and the time-step $\Delta t$
is investigated in the context of galaxy simulations. For isolated galaxy
models we have performed a convergence study and estimated the numerical
parameters ranges for which the relaxed models do not deviate significantly
from its initial configuration. By fixing N, we calculate the range of the mean
interparticle separation $\lambda(r)$ along the disc radius. We have found that
in the simulations with N=1310720 particles $\lambda$ varies by a factor of 6,
and the corresponding final Toomre's parameters Q change by only about 5 per
cent. By decreasing N, the $\lambda$ and Q ranges broaden. Large $\epsilon$ and
small N cause an earlier bar formation. For a given set of parameters the disc
heating is smaller with the Plummer softening than with the spline softening.
For galaxy collision models numerical simulations indicate that the properties
of the formed bars strongly depend upon the selection of N and $\epsilon$.
Large values of the gravitational softening parameter and a small number of
particles results in the rapid formation of a well defined, slowly rotating
bar. On the other hand, small values of $\epsilon$ produce a small, rapidly
rotating disc with tightly wound spiral arms, and subsequently a weak bar
emerges. We have found that by increasing N, the bar properties converge and
the effect of the softening parameter diminishes. Finally, in some cases short
spiral arms are observed at the ends of the bar that change periodically from
trailing to leading and vice-versa - the wiggle.
