Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

Handle URI:
http://hdl.handle.net/10754/600188
Title:
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Authors:
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
Abstract:
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Abdulle A, Vilmart G, Zygalakis KC (2013) Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations. SIAM Journal on Scientific Computing 35: A1792–A1814. Available: http://dx.doi.org/10.1137/12088954X.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2013
DOI:
10.1137/12088954X
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author's work was partially supported by Swiss National Foundation Grant 200021_140692.This author's work was partially supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorAbdulle, Assyren
dc.contributor.authorVilmart, Gillesen
dc.contributor.authorZygalakis, Konstantinos C.en
dc.date.accessioned2016-02-28T06:44:45Zen
dc.date.available2016-02-28T06:44:45Zen
dc.date.issued2013-01en
dc.identifier.citationAbdulle A, Vilmart G, Zygalakis KC (2013) Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations. SIAM Journal on Scientific Computing 35: A1792–A1814. Available: http://dx.doi.org/10.1137/12088954X.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/12088954Xen
dc.identifier.urihttp://hdl.handle.net/10754/600188en
dc.description.abstractWe introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author's work was partially supported by Swiss National Foundation Grant 200021_140692.This author's work was partially supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectExplicit stochastic methodsen
dc.subjectOrthogonal Runge- Kutta-Chebysheven
dc.subjectS-ROCKen
dc.subjectStabilized methodsen
dc.subjectStiff SDEsen
dc.titleWeak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionEcole Polytechnique Federale de Lausanne, Lausanne, Switzerlanden
dc.contributor.institutionEcole Normale Superieure de Cachan, Cachan, Franceen
dc.contributor.institutionUniversity of Southampton, Southampton, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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