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

Type
Article

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

KAUST Grant Number
KUK-C1-013-04

Date
2012-01

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.

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).

Publisher
Society for Industrial & Applied Mathematics (SIAM)

Journal
SIAM Journal on Scientific Computing

DOI
10.1137/110846609

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