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A quasi-Monte Carlo method for the Boltzmann equation

Author: Christian Lécot
Journal: Math. Comp. 56 (1991), 621-644
MSC: Primary 65C05; Secondary 76M25, 76P05, 82C40
MathSciNet review: 1068812
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Abstract: A new quasi-Monte Carlo method for solving the Boltzmann equation in a simplified case is described. The analysis is restricted to a spatially homogeneous and isotropic gas; in addition, the molecular model only involves isotropic scattering. The scheme makes use of particles and combines an Euler scheme with numerical integrations. The sequence which is used for the quadratures must possess some symmetry properties which prescribe energy conservation for colliding particles. The error of the method is estimated by means of the discrepancy of the sequence which performs the quadratures. An algorithm for generating convenient sequences is proposed. In an example, where an exact solution is known, the computation of effective errors is included.

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Article copyright: © Copyright 1991 American Mathematical Society