High weak order methods for stochastic equations based on modified equations

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 (mean-square 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.


Publié dans:
SIAM Journal of Scientific Computing, 34, 3, 1800-1823
Année
2012
Publisher:
Philadelphia, Siam Publications
ISSN:
1064-8275
Mots-clefs:
Laboratoires:




 Notice créée le 2012-11-06, modifiée le 2018-01-28

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