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High weak order methods for stochastic differential equations based on modified equations
Institut für Angewandte und Numerische Mathematik, KIT.
2012 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 3, A1800-A1823 p.Article in journal (Refereed) Published
Abstract [en]

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 firstintegrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

Place, publisher, year, edition, pages
2012. Vol. 34, no 3, A1800-A1823 p.
Keyword [en]
weak convergence, modified equations, backward error analysis, stiff integrator, invariant preserving integrator
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-59180DOI: 10.1137/110846609OAI: diva2:551394
Available from: 2012-09-11 Created: 2012-09-11 Last updated: 2012-10-22Bibliographically approved

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Cohen, David
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