Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

Assyr Abdulle; Gilles Vilmart; Konstantinos C. Zygalakis

doi:10.1137/12088954X

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

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.

Original language	English (US)
Pages (from-to)	A1792-A1814
Number of pages	1
Journal	SIAM Journal on Scientific Computing
Volume	35
Issue number	4
DOIs	https://doi.org/10.1137/12088954X
State	Published - Jan 2013
Externally published	Yes

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10.1137/12088954X

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title = "Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations",

abstract = "We introduce a new family of explicit integrators for stiff It{\^o} 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. {\textcopyright} 2013 Society for Industrial and Applied Mathematics.",

author = "Assyr Abdulle and Gilles Vilmart and Zygalakis, {Konstantinos C.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2013",

month = jan,

doi = "10.1137/12088954X",

language = "English (US)",

volume = "35",

pages = "A1792--A1814",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

AU - Abdulle, Assyr

AU - Vilmart, Gilles

AU - Zygalakis, Konstantinos C.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/1

Y1 - 2013/1

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/600188

UR - http://epubs.siam.org/doi/10.1137/12088954X

UR - http://www.scopus.com/inward/record.url?scp=84886808370&partnerID=8YFLogxK

U2 - 10.1137/12088954X

DO - 10.1137/12088954X

M3 - Article

SN - 1064-8275

VL - 35

SP - A1792-A1814

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 4

ER -

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

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