Global weighted Monte Carlo method for the nonlinear Boltzmann equation

New weighted modifications of direct statistical simulation methods as applied to the nonlinear Boltzmann equation are developed on the basis of an original strategy–stratification of the collision distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated on a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the number of particles in the simulating ensemble.