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Published Online: 12 June 2007
Accepted: May 2007

Adaptive explicit-implicit tau-leaping method with automatic tau selection

J. Chem. Phys. 126, 224101 (2007); https://doi.org/10.1063/1.2745299
Yang Caoa)
  • Department of Computer Science, 660 McBryde Hall, Virginia Tech, Blacksburg, Virginia 24061
    • Daniel T. Gillespie
  • Dan T. Gillespie Consulting, 30504 Cordoba Place, Castaic, California 91384
    • Linda R. Petzold
  • Department of Computer Science, University of California, Santa Barbara, California 93106
    • more...View Affiliations
    ABSTRACT
    The existing tau-selection strategy, which was designed for explicit tau leaping, is here modified to apply to implicit tau leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency is proposed. Numerical testing demonstrates the advantages of the adaptive method for stiff systems.

    ACKNOWLEDGMENTS

    Support for two of the authors (L.R.P. and Y.C.) was provided by the U. S. Department of Energy under DOE Award No. DE-FG02-04ER25621, by the National Science Foundation under NSF Award Nos. CCF-0326576 and NSF∕NIGMS GM078993, by the Institute for Collaborative Biotechnologies through Grant No. DAAD19-03-D-0004 from the U. S. Army Research Office, and by NIH GM075297 and NIH GM078989. Support for one of the authors (D.T.G.) was provided by the University of California under Consulting Agreement 054281A20 with the Computer Science Department of its Santa Barbara campus; and by the California Institute of Technology, through Consulting Agreement 21E-1079702 with the Beckman Institute’s Biological Network Modeling Center, and through Consulting Agreement 102-1080890 with the Control and Dynamical Systems Department pursuant to NIH Grant No. R01 GM078992 from the National Institute of General Medical Sciences.

    REFERENCES
    Section:
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    1. 1. H. McAdams and A. Arkin, Proc. Natl. Acad. Sci. U.S.A. https://doi.org/10.1073/pnas.94.3.814 94, 814 (1997). Google ScholarCrossref
    2. 2. A. Arkin, J. Ross, and H. McAdams, Genetics 149, 1633 (1998). Google Scholar
    3. 3. H. H. McAdams and A. Arkin, Trends Genet. https://doi.org/10.1016/S0168-9525(98)01659-X 15, 65 (1999). Google ScholarCrossref
    4. 4. N. Fedoroff and W. Fontana, Science https://doi.org/10.1126/science.1075988 297, 1129 (2002). Google ScholarCrossref
    5. 5. D. Gillespie, J. Comput. Phys. https://doi.org/10.1016/0021-9991(76)90041-3 22, 403 (1976). Google ScholarCrossref
    6. 6. D. Gillespie, J. Phys. Chem. https://doi.org/10.1021/j100540a008 81, 2340 (1977). Google ScholarCrossref
    7. 7. M. Gibson and J. Bruck, J. Phys. Chem. A https://doi.org/10.1021/jp993732q 104, 1876 (2000). Google ScholarCrossref
    8. 8. Y. Cao, H. Li, and L. Petzold, J. Chem. Phys. https://doi.org/10.1063/1.1778376 121, 4059 (2004). Google ScholarScitation, ISI
    9. 9. D. Gillespie, J. Chem. Phys. https://doi.org/10.1063/1.1378322 115, 1716 (2001). Google ScholarScitation, ISI
    10. 10. Y. Cao, L. Petzold, M. Rathinam, and D. Gillespie, J. Chem. Phys. https://doi.org/10.1063/1.1823412 121, 12169 (2004). Google ScholarScitation
    11. 11. M. Rathinam, L. Petzold, Y. Cao, and D. Gillespie, J. Chem. Phys. https://doi.org/10.1063/1.1627296 119, 12784 (2003). Google ScholarScitation, ISI
    12. 12. Y. Cao and L. Petzold, Proc. FOSBE 2005, Santa Barbara, CA, pp. 149–152, 2005. Google Scholar
    13. 13. M. Rathinam, L. Petzold, Y. Cao, and D. Gillespie, Multiscale Modeling & Simulation: A SIAM Interdisciplinary Journal 4, 867 (2005). Google ScholarCrossref
    14. 14. Y. Cao, D. Gillespie, and L. Petzold, J. Chem. Phys. https://doi.org/10.1063/1.2159468 124, 044109 (2006). Google ScholarScitation, ISI
    15. 15. J. D. Ramshaw, Phys. Fluids 23, 675 (1980). Google ScholarScitation
    16. 16. M. Rein, Phys. Fluids A 4, 873 (1992). Google ScholarScitation
    17. 17. L. A. Segel and M. Slemrod, SIAM Rev. 31, 446 (1989). Google ScholarCrossref
    18. 18. C. Rao and A. Arkin, J. Chem. Phys. https://doi.org/10.1063/1.1545446 118, 4999 (2003). Google ScholarScitation
    19. 19. Y. Cao, D. Gillespie, and L. Petzold, J. Chem. Phys. https://doi.org/10.1063/1.1824902 122, 014116 (2005). Google ScholarScitation
    20. 20. L. Petzold, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 4, 136 (1983). Google ScholarCrossref
    21. 21. K. Radhakrishnan and A. C. Hindmarsh, LLNL Report No. UCRL-ID-113855, 1993 (unpublished). Google Scholar
    22. 22. T. Tian and K. Burrage, J. Chem. Phys. https://doi.org/10.1063/1.1810475 121, 10356 (2004). Google ScholarScitation
    23. 23. A. Chatterjee, D. G. Vlachos, and M. A. Katsoulakis, J. Chem. Phys. https://doi.org/10.1063/1.1833357 122, 024112 (2005). Google ScholarScitation, ISI
    24. 24. M. Pettigrew and H. Resat, J. Chem. Phys. https://doi.org/10.1063/1.2432326 126, 084101 (2007). Google ScholarScitation
    25. 25. Y. Cao, D. Gillespie, and L. Petzold, J. Chem. Phys. https://doi.org/10.1063/1.1992473 123, 054104 (2005). Google ScholarScitation
    26. 26. D. Gillespie and L. Petzold, J. Chem. Phys. https://doi.org/10.1063/1.1613254 119, 8229 (2003). Google ScholarScitation
    27. 27. A. Samant and D. G. Vlachos, J. Chem. Phys. https://doi.org/10.1063/1.2046628 123, 144114 (2005). Google ScholarScitation, ISI
    28. 28. Y. Cao, D. Gillespie, and L. Petzold, J. Comput. Phys. https://doi.org/10.1016/j.jcp.2004.12.014 206, 395 (2005). Google ScholarCrossref
    29. 29. Y. Cao and L. Petzold, J. Comput. Phys. https://doi.org/10.1016/j.jcp.2005.06.012 212, 6 (2006). Google ScholarCrossref
    30. 30. R. Bundschuh, F. Hayot, and C. Jayaprakash, J. Theor. Biol. https://doi.org/10.1006/jtbi.2003.3164 220, 261 (2003). Google ScholarCrossref
    31. 31. L. Michaelis and M. L. Menten, Biochem. Z. 49, 333 (1913). Google Scholar
    32. 32. K. M. Plowman, Enzyme Kinetics (McGraw-Hill, New York, 1971). Google Scholar
    33. 33. Y. Cao, D. Gillespie, and L. Petzold, J. Chem. Phys. https://doi.org/10.1063/1.2052596 123, 144917 (2005). Google ScholarScitation
    34. © 2007 American Institute of Physics.

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