  Monte Carlo simulations of the short-time dynamic behavior are reported for
three-dimensional weakly site-diluted Ising model with spin concentrations
$p=0.95$ and 0.8 at criticality. In contrast to studies of the critical
behavior of the pure systems by the short-time dynamics method, our
investigations of site-diluted Ising model have revealed three stages of the
dynamic evolution characterizing a crossover phenomenon from the critical
behavior typical for the pure systems to behavior determined by the influence
of disorder. The static and dynamic critical exponents are determined with the
use of the corrections to scaling for systems starting separately from ordered
and disordered initial states. The obtained values of the exponents demonstrate
a universal behavior of weakly site-diluted Ising model in the critical region.
The values of the exponents are compared to results of numerical simulations
which have been obtained in various works and, also, with results of the
renormalization-group description of this model.
