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 
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/
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     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/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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