Multilevel hybrid split-step implicit tau-leap

Embargo End Date
2017-06-17

Type
Article

Authors
Ben Hammouda, Chiheb
Moraes, Alvaro
Tempone, Raul

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program

Online Publication Date
2016-06-17

Print Publication Date
2017-02

Date
2016-06-17

Abstract
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Here, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method.

Citation
Ben Hammouda C, Moraes A, Tempone R (2016) Multilevel hybrid split-step implicit tau-leap. Numerical Algorithms. Available: http://dx.doi.org/10.1007/s11075-016-0158-z.

Acknowledgements
Clean Combustion Center at King Abdullah University of Science and Technology

Publisher
Springer Science and Business Media LLC

Journal
Numerical Algorithms

DOI
10.1007/s11075-016-0158-z

arXiv
1512.00721

Additional Links
http://arxiv.org/pdf/1512.00721

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