Effectiveness of implicit methods for stiff stochastic differential equations

Tiejun Li, Assyr Abdulle, E. Weinan

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales. We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale. This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.

Original languageEnglish (US)
Pages (from-to)295-307
Number of pages13
JournalCommunications in Computational Physics
Issue number2
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


  • Implicity methods
  • Invariant distribution
  • Multiscale
  • Stiff ODE
  • Stiff SDE


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