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

Assyr Abdulle; David Cohen; Gilles Vilmart; Konstantinos C. Zygalakis

doi:10.1137/110846609

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

Assyr Abdulle, David Cohen, Gilles Vilmart, Konstantinos C. Zygalakis

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

46 Scopus citations

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.

Original language	English (US)
Pages (from-to)	A1800-A1823
Number of pages	1
Journal	SIAM Journal on Scientific Computing
Volume	34
Issue number	3
DOIs	https://doi.org/10.1137/110846609
State	Published - Jan 2012
Externally published	Yes

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title = "High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations",

abstract = "{\textcopyright} 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.",

author = "Assyr Abdulle and David Cohen 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 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Abdulle, Assyr

AU - Cohen, David

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 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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N2 - © 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.

AB - © 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.

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

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