High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

Handle URI:
http://hdl.handle.net/10754/598483
Title:
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Authors:
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
Abstract:
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.
Citation:
Abdulle A, Cohen D, Vilmart G, Zygalakis KC (2012) High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations. SIAM Journal on Scientific Computing 34: A1800–A1823. Available: http://dx.doi.org/10.1137/110846609.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2012
DOI:
10.1137/110846609
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author's work was partially supported under Swiss National Foundation grant 200021_140692.This author's work was supported by award KUK-C1-013-04 of the King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAbdulle, Assyren
dc.contributor.authorCohen, Daviden
dc.contributor.authorVilmart, Gillesen
dc.contributor.authorZygalakis, Konstantinos C.en
dc.date.accessioned2016-02-25T13:30:47Zen
dc.date.available2016-02-25T13:30:47Zen
dc.date.issued2012-01en
dc.identifier.citationAbdulle A, Cohen D, Vilmart G, Zygalakis KC (2012) High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations. SIAM Journal on Scientific Computing 34: A1800–A1823. Available: http://dx.doi.org/10.1137/110846609.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/110846609en
dc.identifier.urihttp://hdl.handle.net/10754/598483en
dc.description.abstract© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.en
dc.description.sponsorshipThis author's work was partially supported under Swiss National Foundation grant 200021_140692.This author's work was supported by award KUK-C1-013-04 of the King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBackward error analysisen
dc.subjectInvariant preserving integratoren
dc.subjectModified equationsen
dc.subjectStiff integratoren
dc.subjectWeak convergenceen
dc.titleHigh Weak Order Methods for Stochastic Differential Equations Based on Modified Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionEcole Polytechnique Federale de Lausanne, Lausanne, Switzerlanden
dc.contributor.institutionKarlsruhe Institute of Technology, Karlsruhe, Germanyen
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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