Geodesic
Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 715-726
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number $N_0$ of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is $O(N_0^{-1})$. Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient. 
@article{ZVMMF_2006_46_4_a12,
     author = {G. A. Mikhailov and S. V. Rogazinskii and N. M. Ureva},
     title = {Weighted {Monte} {Carlo} method for an approximate solution of the nonlinear coagulation equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {715--726},
     year = {2006},
     volume = {46},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a12/}
}
TY  - JOUR
AU  - G. A. Mikhailov
AU  - S. V. Rogazinskii
AU  - N. M. Ureva
TI  - Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 715
EP  - 726
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a12/
LA  - ru
ID  - ZVMMF_2006_46_4_a12
ER  - 
%0 Journal Article
%A G. A. Mikhailov
%A S. V. Rogazinskii
%A N. M. Ureva
%T Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 715-726
%V 46
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a12/
%G ru
%F ZVMMF_2006_46_4_a12
G. A. Mikhailov; S. V. Rogazinskii; N. M. Ureva. Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 715-726. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a12/

[1] Ivanov M. S., Korotchenko M. A., Mikhailov G. A., Rogazinskii S. V., “Globalno-vesovoi metod Monte-Karlo dlya nelineinogo uravneniya Boltsmana”, Zh. vychisl. matem. i matem. fiziki, 45:10 (2005), 1860–1870 | MR | Zbl

[2] Gillespie D. J., “The stochastic coalescence model for cloud droplet growth”, J. Atmospheric Sci., 29:8 (1972), 1496–1510 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[3] Lushnikov A. A., “Nekotorye novye aspekty teorii koagulyatsii”, Izv. AN SSSR. Fiz. atmosfery i okeana, 14:10 (1978), 1048–1055

[4] Marcus A. H., “Stochastic coalescence”, Technometrics, 10:1 (1968), 133–143 | DOI | MR

[5] Mikhailov G. A., Rogazinskii S. V., “Vesovye metody Monte-Karlo dlya priblizhennogo resheniya nelineinogo uravneniya Boltsmana”, Sibirskii matem. zhurnal, 43:3 (2002), 620–628 | MR

[6] Kats M., Veroyatnost i smezhnye voprosy v fizike, Mir, M., 1965 | Zbl

[7] Rogazinskii S. V., “Ob odnom podkhode k resheniyu odnorodnogo uravneniya Boltsmana”, Zh. vychisl. matem. i matem. fiziki, 27:4 (1987), 564–574 | MR

[8] Ermakov S. M., Mikhailov G. A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR

[9] Domilovskii E. R., Dushnikov A. A., Piskunov V. N., “Modelirovanie protsessov koagulyatsii metodom Monte-Karlo”, Dokl. AN SSSR, 240:41 (1978), 108–110

[10] Mikhailov G. A., Vesovye algoritmy statisticheskogo modelirovaniya, IVMiMG SO RAN, Novosibirsk, 2003

[11] Mikhailov G. A., Vesovye metody Monte-Karlo, IVMiMG SO RAN, Novosibirsk, 2000 | MR

[12] Voloschuk V. M., Kineticheskaya teoriya koagulyatsii, Gidrometeoizdat, L., 1984