Articles | Volume 15, issue 21
https://doi.org/10.5194/acp-15-12315-2015
https://doi.org/10.5194/acp-15-12315-2015
Research article
 | 
06 Nov 2015
Research article |  | 06 Nov 2015

An algorithm for the numerical solution of the multivariate master equation for stochastic coalescence

L. Alfonso

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Cited articles

Alfonso, L., Raga, G. B., and Baumgardner, D.: The validity of the kinetic collection equation revisited – Part 3: Sol–gel transition under turbulent conditions, Atmos. Chem. Phys., 13, 521–529, https://doi.org/10.5194/acp-13-521-2013, 2013.
Bayewitz, M. H., Yerushalmi, J., Katz, S., and Shinnar, R.: The extent of correlations in a stochastic coalescence process, J. Atmos. Sci., 31, 1604–1614, 1974.
Bellman, R. E.: Adaptive control processes: A guided tour, Princeton University Press, Princeton, NJ, 1961.
Gillespie, D. T.: An Exact Method for Numerically Simulating the Stochastic Coalescence Process in a Cloud, J. Atmos. Sci. 32, 1977–1989, 1975.
Gillespie, D. T.: Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81, 2340–2361, 1977.
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Short summary
The mathematical description of finite volume coalescing systems relies on the multivariate master equation. However, due to its complexity, it has analytical solutions only for a limited number of kernels and initial conditions. In this paper, in an effort to solve this problem, we have introduced a novel numerical approach to calculate the solution of the multivariate coalescence master equation that works for any type of kernel and initial conditions.
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