"A fast numerical method for solving the Smoluchowski-type kinetic equations of aggregation and fragmentation processes"
Matveev S.A., Tyrtyshnikov E.E., Smirnov A.P., and Brilliantov N.V.

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.

  • Matveev S.A. – Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics; Leninskie Gory, Moscow, 119992, Russia; Student, e-mail: matveevserega@rambler.ru
  • Tyrtyshnikov E.E. – Institute of Numerical Mathematics, Russian Academy of Sciences; ulitsa Gubkina 8, Moscow, 119333, Russia; Professor, Director, e-mail: eugene.tyrtyshnikov@gmail.com
  • Smirnov A.P. – Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics; Leninskie Gory, Moscow, 119992, Russia; Associate Professor, e-mail: sap@cs.msu.su
  • Brilliantov N.V. – Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH United Kingdom; Professor, e-mail: nb144@leicester.ac.uk