Study and optimization of \(N\)-particle numerical statistical algorithm for solving the Boltzmann equation. (English) Zbl 07866005
Summary: The main goal of this work is to check the hypothesis that the well-known \(N\)-particle statistical algorithm yields a solution estimate for the nonlinear Boltzmann equation with an \(O(1/N)\) error. For this purpose, practically important optimal relations between \(N\) and the number \(n\) of sample estimate values are determined. Numerical results for a problem with a known solution confirm that the formulated estimates and conclusions are satisfactory.
Keywords:
Monte Carlo method; statistical modeling; Boltzmann equation; \(N\)-particle Markov chain; molecular chaos; majorizing frequency methodReferences:
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