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Numerical methods and programming, 2018, Volume 19, Issue 3, Pages 261–269
(Mi vmp918)
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An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions
D. A. Stefonishina, S. A. Matveevb, A. P. Smirnova, E. E. Tyrtyshnikovc a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Skolkovo Institute of Science and Technology
c Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow
Abstract:
We consider a model of aggregation processes for the Smoluchowski-type kinetic equations with three-body collisions of particles. We propose a numerical method for the fast solving of Cauchy problems for the corresponding systems of equations. The proposed method allows one to reduce the step complexity $O (N^{3})$ of the finite-difference predictor-corrector scheme to $O (RN\log N)$ without loss of accuracy. Here the parameter $N$ specifies the number of considered equations and $R$ is the rank of kinetic coefficient arrays. The efficiency and accuracy of the proposed numerical method are demonstrated for model problems of aggregation kinetics.
Keywords:
three-body Smoluchowski equation, kinetics of aggregation processes, predictor-corrector scheme, low-rank tensor approximations, discrete convolution.
Received: 30.04.2018
Citation:
D. A. Stefonishin, S. A. Matveev, A. P. Smirnov, E. E. Tyrtyshnikov, “An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions”, Num. Meth. Prog., 19:3 (2018), 261–269
Linking options:
https://www.mathnet.ru/eng/vmp918 https://www.mathnet.ru/eng/vmp/v19/i3/p261
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Abstract page: | 225 | Full-text PDF : | 72 |
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