Uniformly accurate schemes for drift--oscillatory stochastic differential equations

Ibrahim Almuslimani (1, 2) , Philippe Chartier (3, 2) , Mohammed Lemou (1) , Florian Méhats (1)

1 MINGUS - Multi-scale numerical geometric schemes
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Inria Rennes – Bretagne Atlantique

In this work, we adapt the micro-macro methodology to stochastic differential equations for the purpose of numerically solving oscillatory evolution equations. The models we consider are addressed in a wide spectrum of regimes where oscillations may be slow or fast. We show that through an ad-hoc transformation (the micro-macro decomposition), it is possible to retain the usual orders of convergence of Euler-Maruyama method, that is to say, uniform weak order one and uniform strong order one half.

Mots clés: highly-oscillatory; stochastic differential equations; micro-macro decomposition; uniform accuracy

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Ibrahim Almuslimani, Philippe Chartier, Mohammed Lemou, Florian Méhats. Uniformly accurate schemes for drift--oscillatory stochastic differential equations. Applied Numerical Mathematics, 2022, 468-482, pp.468-482. ⟨10.1016/j.apnum.2022.07.001⟩. ⟨hal-03371466v3⟩