  We present numerical simulation of bulk Lorentz factor of relativistic
electron-positron jet driven by Compton rocket effect from accretion disc
radiation. The plasma is assumed to have a power-law distribution
$n_{e}(\gamma) \propto \gamma^{-s}$ whith $1 < \gamma< \gamma_{max}$ and is
continuously reheated to compensate for radiation losses. We include full
Klein-Nishina (hereafter KN) cross section, and study the role of energy upper
cut-off $\gamma_{max}$, spectral index $s$, and source compactness. We
determine terminal bulk Lorentz factor in the case of supermassive black holes
relevant to AGN and stellar black holes relevant to galactic microquasars. In
the latter case, Klein-Nishina cross section effect are more important, and
induce terminal bulk Lorentz factor smaller than in the former case. Our result
are in good agreement with bulk Lorentz factors observed in galactic sources
(GRS1915+105, GROJ1655-40) and extragalactic ones. Differences in scattered
radiation and acceleration mechanism efficiency in AGN environment can be
responsible for the variety of relativistic motion in those objects. We also
take into account the influence of the size of the accretion disc; if the
external radius is small enough, the bulk Lorentz factor can be as high as 60.

Astrophysics