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Postprocessed Integrators for the High Order Integration of Ergodic SDEs

Published in SIAM Journal on Scientific Computing. 2015, vol. 37, no. 1, p. A201-A220
Abstract The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a numerical method by using an appropriate change of variables called the processor. We show that this technique can be extended to the stochastic context for the construction of new high order integrators for the sampling of the invariant measure of ergodic systems. The approach is illustrated with modifications of the stochastic $ heta$-method applied to Brownian dynamics, where postprocessors achieving order two are introduced. Numerical experiments, including stiff ergodic systems, illustrate the efficiency and versatility of the approach.
Keywords Stochastic differential equationsEffective orderPostprocessorModified differential equationsInvariant measureErgodicity
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VILMART, Gilles. Postprocessed Integrators for the High Order Integration of Ergodic SDEs. In: SIAM Journal on Scientific Computing, 2015, vol. 37, n° 1, p. A201-A220. doi: 10.1137/140974328 https://archive-ouverte.unige.ch/unige:79277

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Deposited on : 2016-01-13

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