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Vychisl. Metody Programm., 2014, Volume 15, Issue 1, Pages 1–8 (Mi vmp225)  

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

S. A. Matveeva, E. E. Tyrtyshnikovb, A. P. Smirnova, N. V. Brilliantovc

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

Full text: PDF file (196 kB)

Document Type: Article
UDC: 519.6
Received: 25.12.2013

Citation: 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”, Vychisl. Metody Programm., 15:1 (2014), 1–8

Citation in format AMSBIB
\Bibitem{MatTyrSmi14}
\by S.~A.~Matveev, E.~E.~Tyrtyshnikov, A.~P.~Smirnov, N.~V.~Brilliantov
\paper A fast numerical method for solving the Smoluchowski-type kinetic equations of aggregation and fragmentation processes
\jour Vychisl. Metody Programm.
\yr 2014
\vol 15
\issue 1
\pages 1--8
\mathnet{http://mi.mathnet.ru/vmp225}


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