Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics

Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis

Research output: Contribution to journalArticlepeer-review

Abstract

A new characterization of sufficient conditions for the Lie--Trotter splitting to capture the numerical invariant measure of nonlinear ergodic Langevin dynamics up to an arbitrary order is discussed. Our characterization relies on backward error analysis and needs weaker assumptions than assumed so far in the literature. In particular, neither high weak order of the splitting scheme nor symplecticity are necessary to achieve high order approximation of the invariant measure of the Langevin dynamics. Numerical experiments confirm our theoretical findings.


Read More: http://epubs.siam.org/doi/10.1137/140962644
Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalSiam journal on numerical analysis
Volume53
Issue number1
DOIs
Publication statusPublished - 8 Jan 2015

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