On two numerical schemes of the Monte Carlo method for solving the Boltzmann equation

Two numerical schemes of the Monte Carlo method for solving the Cauchy problem for the Boltzmann equation are constructed and tested. They are based on a well-known relationship between a nonlinear integral equation and a random process. Procedures for modeling special random processes on whose trajectories unbiased estimators for the solution are described. Each scheme has its own domain of applicability, in which its advantages manifest themselves. The conjugate scheme is convenient for calculating the Boltzmann distribution function at high velocities (on "tails"). For the example of the BKW solution, the applicability of the schemes is numerically analyzed. © 2010 Allerton Press, Inc.