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Title

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

Authors
Zygalakis, Konstantinos C.
Published in SIAM Journal on Scientific Computing. 2012, vol. 34, no. 3, p. A1800-A1823
Abstract 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.
Keywords Weak convergenceModified equationsBackward error analysisStiff integratorInvariant preserving integrator
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ABDULLE, Assyr et al. High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations. In: SIAM Journal on Scientific Computing, 2012, vol. 34, n° 3, p. A1800-A1823. https://archive-ouverte.unige.ch/unige:41947

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Deposited on : 2014-11-18

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