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Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations

Published in SIAM Journal on Scientific Computing. 2020, vol. 42, no. 1, p. A115-A139
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 Schrödinger 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.
Keywords Highly-oscillatory stochastic differential equationsNonlinear Schrödinger equationWhite noise dispersionGeometric integrationQuadratic first integral
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Research group Analyse numérique
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LAURENT, Adrien, VILMART, Gilles. Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations. In: SIAM Journal on Scientific Computing, 2020, vol. 42, n° 1, p. A115-A139. doi: 10.1137/19M1243075 https://archive-ouverte.unige.ch/unige:133525

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Deposited on : 2020-03-30

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