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M. A. Marchenko
Majorant frequency principle for an approximate solution of a nonlinear spatially inhomogeneous coagulation equation by the Monte Carlo method
We propose an efficient algorithm in the direct statistical simulation method for an approximate solution to the Cauchy problem for a nonlinear spatially inhomogeneous coagulation equation that describes the coagulation of particles together with their diffusion transfer. The use of the majorant frequency principle allows one to attain a linear dependence of the computational costs of the algorithm on the initial number of test particles. The main properties of the algorithm include a special markovian random process and a splitting scheme with respect to physical processes.
We consider in detail the spatially one-dimensional case of the above equation. For this case, we develop a special procedure for transforming the ensemble of test particles and propose a method for the preliminary estimation of the parameters of the computational algorithm.
Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter
Print ISSN: 0927-6467
Volume: 21, 05/2006
Pages: 199 - 218