Towards automatic global error control: Computable weak error expansion for the tau-leap method
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Stochastic Numerics Research Group
Date
2011-01Preprint Posting Date
2010-04-17Permanent link to this record
http://hdl.handle.net/10754/561695
Metadata
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This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms, a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie Algorithm or the Stochastic Simulation Slgorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term. © de Gruyter 2011.Citation
Karlsson, J., & Tempone, R. (2011). Towards automatic global error control: Computable weak error expansion for the tau-leap method. Monte Carlo Methods and Applications, 17(3). doi:10.1515/mcma.2011.011Publisher
Walter de Gruyter GmbHarXiv
1004.2948Additional Links
http://arxiv.org/abs/arXiv:1004.2948v3ae974a485f413a2113503eed53cd6c53
10.1515/MCMA.2011.011