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An adaptive time step scheme for a system of stochastic differential equations with multiple multiplicative noise: Chemical Langevin equation, a proof of concept

J. Chem. Phys. 128, 014103 (2008); doi:10.1063/1.2812240

Published 2 January 2008

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Vassilios Sotiropoulos and Yiannis N. Kaznessis
Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
Models involving stochastic differential equations (SDEs) play a prominent role in a wide range of applications where systems are not at the thermodynamic limit, for example, biological population dynamics. Therefore there is a need for numerical schemes that are capable of accurately and efficiently integrating systems of SDEs. In this work we introduce a variable size step algorithm and apply it to systems of stiff SDEs with multiple multiplicative noise. The algorithm is validated using a subclass of SDEs called chemical Langevin equations that appear in the description of dilute chemical kinetics models, with important applications mainly in biology. Three representative examples are used to test and report on the behavior of the proposed scheme. We demonstrate the advantages and disadvantages over fixed time step integration schemes of the proposed method, showing that the adaptive time step method is considerably more stable than fixed step methods with no excessive additional computational overhead. ©2008 American Institute of Physics
History: Received 15 December 2006; accepted 23 October 2007; published 2 January 2008
Permalink: http://link.aip.org/link/?JCPSA6/128/014103/1
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KEYWORDS and PACS

Keywords
PACS
  • 82.20.Uv
    Stochastic theories of rate constants in chemical kinetics
  • 87.10.-e
    General theory and mathematical aspects (biological/medical physics)
  • YEAR: 2008

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ISSN:
0021-9606 (print)   1089-7690 (online)
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