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

The Journal of Chemical Physics
Vassilios Sotiropoulos, Yiannis N Kaznessis

Abstract

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.

References

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Mar 3, 2004·Bioinformatics·Kouichi TakahashiMasaru Tomita
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Nov 20, 2004·The Journal of Chemical Physics·Tianhai Tian, Kevin Burrage
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Mar 3, 2005·The Journal of Chemical Physics·Howard Salis, Yiannis Kaznessis
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Mar 1, 2006·BMC Bioinformatics·Howard SalisYiannis N Kaznessis
Apr 6, 2007·BMC Systems Biology·Vassilios Sotiropoulos, Yiannis N Kaznessis

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Citations

May 16, 2012·The Journal of Chemical Physics·Silvana Ilie, Alexandra Teslya
Aug 1, 2009·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Vassilios SotiropoulosYiannis N Kaznessis
Sep 29, 2011·Chemical Engineering Science·Vassilios Sotiropoulos, Yiannis N Kaznessis
Mar 5, 2016·The Journal of Chemical Physics·Nikolai D PetsevM Scott Shell
Oct 16, 2009·Biotechnology Journal·Yiannis N Kaznessis
May 21, 2015·Journal of Physics. Condensed Matter : an Institute of Physics Journal·James F Lutsko, Miguel A Durán-Olivencia
Apr 8, 2011·Wiley Interdisciplinary Reviews. Systems Biology and Medicine·Yiannis N Kaznessis

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Software Mentioned

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