Smoluchowski aggregation-fragmentation equations: Fast numerical algorithm for steady-state solution

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.