High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

Assyr Abdulle, David Cohen, Gilles Vilmart, Konstantinos C. Zygalakis

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.
Original languageEnglish (US)
Pages (from-to)A1800-A1823
Number of pages1
JournalSIAM Journal on Scientific Computing
Volume34
Issue number3
DOIs
StatePublished - Jan 2012
Externally publishedYes

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