Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation

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 \(O(1{\text{/}}N)\) 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.