Integral tau methods for stiff stochastic chemical systems

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044129_1_online.pdf (1.22 MB)

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https://pubs.aip.org/aip/jcp/article-abstract/134/4/044129/1003723/Integral-tau-methods-for-stiff-stochastic-chemical?redirectedFrom=fulltext

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https://doi.org/10.1063/1.3532768
 http://hdl.handle.net/11603/35809

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Author/Creator ORCID

https://orcid.org/0000-0003-2172-4182

Date

2011-01-28

Type of Work

journal articles
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Citation of Original Publication

Yang, Yushu, Muruhan Rathinam, and Jinglai Shen. “Integral Tau Methods for Stiff Stochastic Chemical Systems.” The Journal of Chemical Physics 134, no. 4 (January 28, 2011): 044129. https://doi.org/10.1063/1.3532768.

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Yang, Yushu, Muruhan Rathinam, and Jinglai Shen. “Integral Tau Methods for Stiff Stochastic Chemical Systems.” The Journal of Chemical Physics 134, no. 4 (January 28, 2011): 044129. https://doi.org/10.1063/1.3532768. and may be found at https://pubs.aip.org/aip/jcp/article-abstract/134/4/044129/1003723/Integral-tau-methods-for-stiff-stochastic-chemical?redirectedFrom=fulltext

Subjects

Abstract

Tau leaping methods enable efficient simulation of discrete stochastic chemical systems. Stiff stochastic systems are particularly challenging since implicit methods, which are good for stiffness, result in noninteger states. The occurrence of negative states is also a common problem in tau leaping. In this paper, we introduce the implicit Minkowski–Weyl tau (IMW-?) methods. Two updating schemes of the IMW-? methods are presented: implicit Minkowski–Weyl sequential (IMW-S) and implicit Minkowski–Weyl parallel (IMW-P). The main desirable feature of these methods is that they are designed for stiff stochastic systems with molecular copy numbers ranging from small to large and that they produce integer states without rounding. This is accomplished by the use of a split step where the first part is implicit and computes the mean update while the second part is explicit and generates a random update with the mean computed in the first part. We illustrate the IMW-S and IMW-P methods by some numerical examples, and compare them with existing tau methods. For most cases, the IMW-S and IMW-P methods perform favorably.