BIT Numerical Mathematics

, Volume 53, Issue 4, pp 827–840 | Cite as

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

Article

Abstract

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 (Debrabant and Rößler, Appl. Numer. Math. 59(3–4):595–607, 2009).

Keywords

Stiff SDEs Drift-implicit stochastic methods Mean-square stability 

Mathematics Subject Classification (2000)

65C30 60H35 65L20 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.ANMC, Section de MathématiquesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.École Normale Supérieure de Cachan, Antenne de Bretagne, INRIA Rennes, IRMAR, CNRSUEBBruzFrance
  3. 3.School of MathematicsUniversity of SouthamptonSouthamptonUK

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