  It is shown that the extremal Reissner-Nordstr\"{o}m black hole, the
non-extremal one with multiple scattering particles, and the Schwarzschild
black hole with radial head-on particles are stable under the collision of the
particles near the horizon, if the back-reaction effect and the effect
generated by gravity of particles are involved. Moreover, the collision near
Reissner-Nordstr\"{o}m black holes with astrophysically typical mass can not
generate the Planck-scale center-of-mass energy. However, the head-on collision
near the typical primordial black hole could just occur at the Planck-energy
scale.
