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Journal Articles SIAM Journal on Numerical Analysis Year : 2015

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

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.
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Dates and versions

hal-00965354 , version 1 (25-03-2014)
hal-00965354 , version 2 (11-09-2014)

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Assyr Abdulle, Gilles Vilmart, Konstantinos Zygalakis. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. SIAM Journal on Numerical Analysis, 2015, 53 (1), pp.1-16. ⟨10.1137/140962644⟩. ⟨hal-00965354v2⟩
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