S. A. Matveev, E. E. Tyrtyshnikov, A. P. Smirnov, N. V. Brilliantov, “A fast numerical method for solving the Smoluchowski-type kinetic equations of aggregation and fragmentation processes”, Num. Meth. Prog., 2014, Volume 15, Issue 1,Pages <nobr>1

A fast numerical method for solving the Smoluchowski-type kinetic equations of aggregation and fragmentation processes

S. A. Matveev^a, E. E. Tyrtyshnikov^b, A. P. Smirnov^a, N. V. Brilliantov^c

^a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow
^c University of Leicester, University Road, Leicester, LE1 7RH United Kingdom

Abstract: A number of models of aggregation-fragmentation processes on the basis of Smoluchowski-type kinetic equations are considered. A new numerical method for the fast solution of this class of problems is proposed. This method allows one to decrease the computational complexity of a problem without loss of accuracy. The application of the method is illustrated by several examples of problems of aggregation-fragmentation kinetics in the cases of interest in practice.

Keywords: Smoluchowski equation, kinetics equations of aggregation and fragmentation processes, predictor-corrector scheme, cross interpolation method, low-rank matrix approximations, discrete convolution.

UDC: 519.6

Received: 25.12.2013