BIT Numerical Mathematics

, Volume 50, Issue 4, pp 797–822

Efficient simulation of discrete stochastic reaction systems with a splitting method


DOI: 10.1007/s10543-010-0286-0

Cite this article as:
Jahnke, T. & Altıntan, D. Bit Numer Math (2010) 50: 797. doi:10.1007/s10543-010-0286-0


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.


Stochastic simulation algorithm Discrete stochastic reaction systems Splitting methods Analytic solution formulas Error bounds Chemical master equation 

Mathematics Subject Classification (2000)

60J75 65L70 47D06 92D25 92C42 

Copyright information

© Springer Science + Business Media B.V. 2010

Authors and Affiliations

  1. 1.Fakultät für Mathematik, Institut für Angewandte und Numerische MathematikKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Institute of Applied Mathematics, Department of Scientific ComputingMiddle East Technical UniversityAnkaraTurkey
  3. 3.Selçuk UniversityKonyaTurkey