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Efficient simulation of discrete stochastic reaction systems with a splitting method

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Abstract

Stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error.

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Authors and Affiliations

  1. Fakultät für Mathematik, Institut für Angewandte und Numerische Mathematik, Karlsruhe Institute of Technology (KIT), Kaiserstr. 93, 76133, Karlsruhe, Germany

    Tobias Jahnke

  2. Institute of Applied Mathematics, Department of Scientific Computing, Middle East Technical University, 06531, Ankara, Turkey

    Derya Altıntan

  3. Selçuk University, Konya, Turkey

    Derya Altıntan

Authors
  1. Tobias Jahnke
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  2. Derya Altıntan
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Correspondence to Tobias Jahnke.

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Communicated by Uri Ascher.

Supported by the “Concept for the Future” of Karlsruhe Institute of Technology within the framework of the German Excellence Initiative, the DFG priority programme SPP 1324 “Mathematische Methoden zur Extraktion quantifizierbarer Information aus komplexen Systemen”, and a grant of the Middle East Technical University, Ankara, Turkey and Selçuk University, Konya, Turkey.

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Jahnke, T., Altıntan, D. Efficient simulation of discrete stochastic reaction systems with a splitting method. Bit Numer Math 50, 797–822 (2010). https://doi.org/10.1007/s10543-010-0286-0

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