Abstract:
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.
Key words:Monte Carlo method, statistical modeling, Boltzmann equation, $N$-particle Markov chain, molecular chaos, majorizing frequency method.
