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A quasi-Monte Carlo scheme for Smoluchowski's coagulation equation
Author(s):
Christian
Lécot;
Wolfgang
Wagner.
Journal:
Math. Comp.
73
(2004),
1953-1966.
MSC (2000):
Primary 65C05;
Secondary 70-08, 82C80
Posted:
January 5, 2004
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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
Email:
Christian.Lecot@univ-savoie.fr
Wolfgang
Wagner
Affiliation:
Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany
Email:
wagner@wias-berlin.de
DOI:
10.1090/S0025-5718-04-01627-8
PII:
S 0025-5718(04)01627-8
Received by editor(s):
November 11, 2002
Received by editor(s) in revised form:
March 14, 2003
Posted:
January 5, 2004
Additional Notes:
Computation was supported by the Centre Grenoblois de Calcul Vectoriel du Commissariat à l'Énergie Atomique, France
Copyright of article:
Copyright
2004,
American Mathematical Society
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