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Mathematics of Computation

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A quasi-Monte Carlo scheme for Smoluchowski's coagulation equation

Authors: Christian Lécot and Wolfgang Wagner
Translated by:
Journal: Math. Comp. 73 (2004), 1953-1966
MSC (2000): Primary 65C05; Secondary 70-08, 82C80
Published electronically: January 5, 2004
MathSciNet review: 2059745
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Abstract: This paper analyzes a Monte Carlo algorithm for solving Smoluchowski's coagulation equation. A finite number of particles approximates the initial mass distribution. Time is discretized and random numbers are used to move the particles according to the coagulation dynamics. Convergence is proved when quasi-random numbers are utilized and if the particles are relabeled according to mass in every time step. The results of some numerical experiments show that the error of the new algorithm is smaller than the error of a standard Monte Carlo algorithm using pseudo-random numbers without reordering the particles.

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Additional Information

Christian Lécot
Affiliation: Laboratoire de Mathématiques, Université de Savoie, Campus scientifique, 73376 Le Bourget-du-Lac cedex, France

Wolfgang Wagner
Affiliation: Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany

Received by editor(s): November 11, 2002
Received by editor(s) in revised form: March 14, 2003
Published electronically: January 5, 2004
Additional Notes: Computation was supported by the Centre Grenoblois de Calcul Vectoriel du Commissariat à l’Énergie Atomique, France
Article copyright: © Copyright 2004 American Mathematical Society