Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Assyr Abdulle (1) , Gilles Vilmart (2, 3) , Konstantinos Zygalakis (4)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 IPSO - Invariant Preserving SOlvers
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 School of Mathematics [Southampton]

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stability properties of the drift-diagonally-implicit methods previously introduced [K. Debrabant and A. Rößler, Appl. Num. Math., 59, 2009].

Mots clés: mean-square stability; Stiff SDEs; drift-implicit stochastic methods; mean-square stability.

Domaines: Analyse numérique [math.NA]

Assyr Abdulle, Gilles Vilmart, Konstantinos Zygalakis. Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. 2012. ⟨hal-00739756v1⟩