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Weighted statistical modelling algorithms with branching and extension of a model ensemble of interacting particles

Abstract A modification of the weighted statistical modelling of the evolution of an ensemble of interacting particles is constructed for approximate solution of a nonlinear kinetic equation. If the auxiliary weight exceeds one, we propose to use randomized branching of trajectory of the model ensemble of particles or its corresponding extension. Numerical analysis of constructed algorithms is performed for specifically formulated model problem on relaxation of a mixture of two gases with very different concentrations.