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arXiv · 1902.01716

Multirevolution integrators for differential equations with fast stochastic oscillations

Adrien Laurent·Gilles Vilmart
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Abstract

We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise. Applications include in particular highly-oscillatory Kubo oscillators and spatial discretizations of the nonlinear Schr\"odinger equation with fast white noise dispersion. We construct a method of weak order two with computational cost and accuracy both independent of the stiffness of the oscillations. A geometric modification that conserves exactly quadratic invariants is also presented.

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Adrien Laurent, Gilles Vilmart. 2019-02-05. Multirevolution integrators for differential equations with fast stochastic oscillations. https://doi.org/10.1137/19m1243075

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