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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2020

Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations

Résumé

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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Dates et versions

hal-04347677 , version 1 (15-12-2023)

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Paternité

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Adrien Laurent, Gilles Vilmart. Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations. SIAM Journal on Scientific Computing, 2020, 42 (1), pp.A115-A139. ⟨10.1137/19M1243075⟩. ⟨hal-04347677⟩
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