  The fireball, the promising model of the gamma-ray burst (GRB), is an opaque
radiation plasma, whose energy is significantly greater than its rest mass. We
numerically simulate the evolution of the fireball heated by the
neutrino-antineutrino annihilation process for the spherically symmetric case.
We also derive analytical energy and momentum deposition rates via neutrino
scattering with thermalized electron-positron pairs in the fireball. In our
simulation the matter is provided around the neutrinosphere before neutrinos
start to be emitted, and the energy is injected during a finite period of time
$t_{\rm dur}$. In the acceleration regime the matter shell is pushed from
behind by radiation pressure. The Lorentz factor of the shell reaches the
maximum value $\eta$ at $r \simeq \eta^2 c t_{\rm dur}$. After the fireball
enters the coasting regime, the velocity distribution in the shell becomes very
flat. The shell expansion rate $d W/dr$ can be much smaller than $\eta^{-2}$.
The runaway of temperature of the fireball due to neutrino scattering with
electron-positron pairs does not occur in most cases. The energy deposition due
to scattering is not so significant.
