  In a new type of percolation phase transition, which was observed in a set of
non-equilibrium models, each new connection between vertices is chosen from a
number of possibilities by an Achlioptas-like algorithm. This causes
preferential merging of small components and delays the emergence of the
percolation cluster. First simulations led to a conclusion that a percolation
cluster in this irreversible process is born discontinuously, by a
discontinuous phase transition, which results in the term "explosive
percolation transition". We have shown that this transition is actually
continuous (second-order) though with an anomalously small critical exponent of
the percolation cluster. Here we propose an efficient numerical method enabling
us to find the critical exponents and other characteristics of this second
order transition for a representative set of explosive percolation models with
different number of choices. The method is based on gluing together the
numerical solutions of evolution equations for the cluster size distribution
and power-law asymptotics. For each of the models, with high precision, we
obtain critical exponents and the critical point.
