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    Towards automatic global error control: Computable weak error expansion for the tau-leap method

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    Type
    Article
    Authors
    Karlsson, Peer Jesper
    Tempone, Raul cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Stochastic Numerics Research Group
    Date
    2011-01
    Preprint Posting Date
    2010-04-17
    Permanent link to this record
    http://hdl.handle.net/10754/561695
    
    Metadata
    Show full item record
    Abstract
    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.2011.011
    Publisher
    Walter de Gruyter GmbH
    Journal
    Monte Carlo Methods and Applications
    DOI
    10.1515/MCMA.2011.011
    arXiv
    1004.2948
    Additional Links
    http://arxiv.org/abs/arXiv:1004.2948v3
    ae974a485f413a2113503eed53cd6c53
    10.1515/MCMA.2011.011
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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