Value modifications of weighted statistical modelling for solving nonlinear kinetic equations
Mariya Korotchenko, Guennady A. Mikhailov, S. V. Rogazinskii · Russian Journal of Numerical Analysis and Mathematical Modelling · 2007
Based on solving test problems for nonlinear kinetic equations, the efficiency of different variants of weighted ‘value’ modelling of evolution of multiparticle ensembles has been studied. Approximations of solutions to model problems for the Boltzmann and Smolukhovsky equations are taken as value functions. It is shown that the most essential gain is achieved for the combination of approximate value modelling of the free path length of the ensemble with value modelling of the number of a pair of interacting particles. The technique developed here may be useful for solving actual problems of coagulation and relaxation of a system of particles, for which the considered model solutions are approximations.