Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales

Weinan E, Di Liu, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


We present an efficient numerical algorithm for simulating chemical kinetic systems with multiple time scales. This algorithm is an improvement of the traditional stochastic simulation algorithm (SSA), also known as Gillespie's algorithm. It is in the form of a nested SSA and uses an outer SSA to simulate the slow reactions with rates computed from realizations of inner SSAs that simulate the fast reactions. The algorithm itself is quite general and seamless, and it amounts to a small modification of the original SSA. Our analysis of such multi-scale chemical kinetic systems allows us to identify the slow variables in the system, derive effective dynamics on the slow time scale, and provide error estimates for the nested SSA. Efficiency of the nested SSA is discussed using these error estimates, and illustrated through several numerical examples.

Original languageEnglish (US)
Pages (from-to)158-180
Number of pages23
JournalJournal of Computational Physics
Issue number1
StatePublished - Jan 20 2007


  • Averaging theorems
  • Chemical kinetic systems
  • Chemical master equations
  • Continuous-time Markov chains
  • Gillespie algorithm
  • Homogenization
  • Kinetic Monte-Carlo
  • Multi-scale computation
  • Multiscale numerical methods
  • Stochastic Petri nets
  • Stochastic modeling

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales'. Together they form a unique fingerprint.

Cite this