  We numerically model the interaction between an expanding fireball and a
stationary external medium whose density is either homogeneous or varies with
distance as a power-law. The evolution is followed until most of the fireball
kinetic energy is converted into internal energy. The density, pressure and
flow Lorentz factor profiles are shown at different stages, including shock and
rarefaction wave reflections, for a fireball of initial bulk Lorentz factor
Gamma = 100, both in the adiabatic and non-adiabatic (radiative) regimes. For
cooling times shorter than the dynamic time, bolometric light-curves are
computed for values of Gamma = 50, 100 and 200. We compare the numerical
light-curves with analytic results, and find that for a homogeneous external
medium there is a simple scaling relationship among light-curves obtained for
different parameters. The light-curves for power-law external densities are
similar in shape to those in the homogeneous case. We discuss the implications
of a comparison of the results with observed Gamma-Ray Burst time histories.
