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Brownian approximation and Monte Carlo simulation of the non-cutoff Kac equation. (English) Zbl 1139.82035

Summary: The non-cutoff Boltzmann equation can be simulated using the direct simulation Monte Carlo (DSMC) method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
60J75 Jump processes (MSC2010)
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