A stochastic particle numerical method for 3D Boltzmann equations without cutoff
Open Access
- 25 October 2001
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 71 (238) , 583-604
Abstract
Using the main ideas of Tanaka, the measure-solution { P t } t \{P_t\}_t of a 3 3 -dimensional spatially homogeneous Boltzmann equation of Maxwellian molecules without cutoff is related to a Poisson-driven stochastic differential equation. Using this tool, the convergence to { P t } t \{P_t\}_t of solutions { P t l } t \{P^l_t\}_t of approximating Boltzmann equations with cutoff is proved. Then, a result of Graham-Méléard is used and allows us to approximate { P t l } t \{P^l_t\}_t with the empirical measure { μ t l , n } t \{\mu ^{l,n}_t\}_t of an easily simulable interacting particle system. Precise rates of convergence are given. A numerical study lies at the end of the paper.Keywords
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