  We propose an efficient and fast numerical algorithm of finding a
\emph{stationary} solution of large systems of aggregation-fragmentation
equations of Smoluchowski type for concentrations of reacting particles. This
method is applicable when the stationary concentrations steeply decreases with
increasing aggregate size, which is fulfilled for the most important cases. We
show that under rather mild restrictions, imposed on the kernel of the
Smoluchowski equation, the following numerical procedure may be used: First, a
complete solution for a relatively small number of equations (a "seed system")
is generated and then the result is exploited in a fast iterative scheme. In
this way the new algorithm allows to obtain a steady-state solution for rather
large systems of equations, by orders of magnitude faster than the standard
schemes.
