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Тезисы докладов

Стохастическое моделирование и методы Монте-Карло

We consider the frequencies polygon method based on the free-path estimator for global solution of the radiative transfer equation under the conditions of plane symmetry. In paper [1] the embedding theorem is used for upper estimating of the error of considered method in {bf C}-metric. Here we consider the limitation of the error in {bf C}-metric and in probability (so-called {bf C}-approach). The upper bound of the error is constructed with the use of the central limit theorem for mutually independent random vectors. On the base of this upper bound the problem of optimization under fixed error level is decided. Thus it is shown that the conditionally optimal cost value is of the following order: $S_{opt} sim alpha^{-3}(- ln alpha),$ where $alpha > 0$ is a given fixed level of the error. Note that in paper [1] on base of the embedding theorem $S_{opt} sim alpha^{-4}$ is obtained. The obtained optimizing relations are tested on the model radiative transfer equation. It is shown that obtained error is less then fixed error level $alpha$. $$;$$ Large {bf References} normalsize $$;$$ [1] Mikhailov G.A. and Plotnikov M.Yu. An estimator "over a run" for a solution of linear and nonlinear radiative transfer equations in the large. // Russian Acad. Sci. Dokl. Math. 1995, Vol. 50, No. 1, pp. 39 - 42.

Примечание. Тезисы докладов публикуются в авторской редакции

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