Mikhailov, G. A.; Korotchenko, M. A.; Rogasinsky, S. V. Importance modeling algorithms for solving nonlinear kinetic equations. (English. Russian original) Zbl 1154.82025 Dokl. Math. 76, No. 1, 502-505 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 1, 26-30 (2007). From the text: We consider importance weighted modifications of statistical simulation for the numerical solution of the nonlinear Smoluchowski and Boltzmann kinetic equations in the spatially homogeneous case. MSC: 82C40 Kinetic theory of gases in time-dependent statistical mechanics 82C22 Interacting particle systems in time-dependent statistical mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 82D60 Statistical mechanics of polymers 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics 60J25 Continuous-time Markov processes on general state spaces PDFBibTeX XMLCite \textit{G. A. Mikhailov} et al., Dokl. Math. 76, No. 1, 502--505 (2007; Zbl 1154.82025); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 1, 26--30 (2007) Full Text: DOI References: [1] M. Kac, Probability and Related Topics in Physical Sciences (Interscience, London, 1959; Mir, Moscow, 1965). · Zbl 0087.33003 [2] G. A. Mikhailov and S. V. Rogasinsky, Sib. Mat. Zh. 43, 620–628 (2002). · doi:10.1023/A:1015467719806 [3] G. A. Mikhailov, S. V. Rogasinsky, and N. M. Ureva, Comput. Math. Math. Phys. 46, 680–690 (2006) [Zh. Vychisl. Mat. Mat. Fiz. 46, 714–725 (2006)]. · doi:10.1134/S0965542506040130 [4] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Simulation (Monte Carlo Method) (Akademiya, Moscow, 2006) [in Russian]. [5] G. I. Marchuk, V. I. Agoshkov, and V. P. Shutyaev, Adjoint Equations and Perturbation Methods in Nonlinear Problems of Mathematical Physics (Nauka, Moscow, 1993) [in Russian]. · Zbl 0869.47036 [6] G. A. Mikhailov, Dokl. Math. 67, 230–233 (2003) [Dokl. Akad. Nauk 389, 461–464 (2003)]. [7] V. M. Voloshchuk, Kinetic Theory of Coagulation (Gidrometeoizdat, Leningrad, 1984) [in Russian]. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.