Geodesic
An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions
Numerical methods and programming, Tome 19 (2018) no. 3, pp. 261-269

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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
Mots-clés : discrete convolution. 
@article{VMP_2018_19_3_a6,
     author = {D. A. Stefonishin and S. A. Matveev and A. P. Smirnov and E. E. Tyrtyshnikov},
     title = {An efficient finite-difference method for solving {Smoluchowski-type} kinetic equations of aggregation with three-body collisions},
     journal = {Numerical methods and programming},
     pages = {261--269},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_3_a6/}
}
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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. Numerical methods and programming, Tome 19 (2018) no. 3, pp. 261-269. http://geodesic.mathdoc.fr/item/VMP_2018_19_3_a6/