  The orbital evolution of asteroids from the 3:1 and 5:2 resonances with
Jupiter under the gravitational influence of planets was investigated both by
the Bulirsh-Stoer method and by a symplectic method. The probabilities of
collisions of asteroids with the terrestrial planets were calculated for
orbital elements obtained with a step of 500 yr. The ratio of asteroids from
the 3:1 resonance that were ejected into hyperbolic orbits to those collided
the Sun was by an order of magnitude larger for direct integrations than for a
symplectic method. The probability of a collision of an asteroid with the Earth
for the 3:1 resonance was by a factor of 4 larger than that for the 5:2
resonance. The ratio of the probability of a collision of a body with a planet
to the mass of the planet for Mars was by a factor of 2 larger than that for
Earth and Venus.
