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A quasi-Monte Carlo method for the coagulation equation. (English) Zbl 1368.11087

Larcher, Gerhard (ed.) et al., Applied algebra and number theory. Essays in honor of Harald Niederreiter on the occasion of his 70th birthday. Cambridge: Cambridge University Press (ISBN 978-1-107-07400-2/hbk; 978-1-139-69645-6/ebook). 216-234 (2014).
Summary: We propose a quasi-Monte Carlo algorithm for the simulation of the continuous coagulation equation. The mass distribution is approximated by a finite number \(N\) of numerical particles. Time is discretized and quasi-random points are used at every time step to determine whether each particle is undergoing a coagulation. Convergence of the scheme is proved when \(N\) goes to infinity, if the particles are relabeled according to their increasing mass at each time step. Numerical tests show that the computed solutions are in good agreement with analytical solutions, when available. Moreover, the error of the QMC algorithm is smaller than the error given by a standard Monte Carlo scheme using the same time step and number \(N\) of numerical particles.
For the entire collection see [Zbl 1314.11002].

MSC:

11K45 Pseudo-random numbers; Monte Carlo methods
45K05 Integro-partial differential equations
11K38 Irregularities of distribution, discrepancy
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