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

Authors

  • S.A. Matveev
  • E.E. Tyrtyshnikov
  • A.P. Smirnov
  • N.V. Brilliantov

Keywords:

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

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.

New computational technologies

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Published

2014-01-15

Issue

Vol. 15 (2014): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

S.A. Matveev

Lomonosov Moscow State University,
Faculty of Computational Mathematics and Cybernetics
• Student

E.E. Tyrtyshnikov

Institute of Numerical Mathematics of RAS (INM RAS)
• Director

A.P. Smirnov

Lomonosov Moscow State University,
Faculty of Computational Mathematics and Cybernetics
• Associate Professor

N.V. Brilliantov

University of Leicester,
Department of Mathematics
• Professor

References

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