On the constant kernel Smoluchowski equation: fast algorithm for solution with arbitrary initial conditions

Despite the progress in solving and understanding the mean-field coagulation equation (Smoluchowski equation) even its simpler form, the constant kernel one, has not been fully explored. The existing solution techniques for this particular problem are reviewed and shown to be incapable to provide fast accurate solution for the complete parametric domain. A new very fast algorithm (based on the so called discrete z-transform) is proposed for the solution of the constant kernel coagulation equation with arbitrarily large accuracy for the complete parametric space. Using the new technique the coagulation equation is solved for some non trivial initial conditions (inaccessible with the existing methods) and the results are presented and discussed.