Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales

Journal Article · Sat Jan 20 04:00:00 EST 2007 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2006.06.019· OSTI ID:20991553

E, Weinan ^[1]; Liu, Di ^[2]; Vanden-Eijnden, Eric ^[3]

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1. Department of Mathematics and PACM, Princeton University, Princeton, NJ 08544 (United States)
2. Department of Mathematics, Michigan State University, East Lansing, MI 48824 (United States)
3. Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States)

We present an efficient numerical algorithm for simulating chemical kinetic systems with multiple time scales. This algorithm is an improvement of the traditional stochastic simulation algorithm (SSA), also known as Gillespie's algorithm. It is in the form of a nested SSA and uses an outer SSA to simulate the slow reactions with rates computed from realizations of inner SSAs that simulate the fast reactions. The algorithm itself is quite general and seamless, and it amounts to a small modification of the original SSA. Our analysis of such multi-scale chemical kinetic systems allows us to identify the slow variables in the system, derive effective dynamics on the slow time scale, and provide error estimates for the nested SSA. Efficiency of the nested SSA is discussed using these error estimates, and illustrated through several numerical examples.

• OSTI ID: 20991553
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 221; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
EQUATIONS
ERRORS
MARKOV PROCESS
MATHEMATICAL MODELS
MONTE CARLO METHOD
SIMULATION