Multirevolution integrators for differential equations with fast
stochastic oscillations
A. Laurent and G. Vilmart
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 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.
Key Words. highly-oscillatory stochastic differential equations, nonlinear Schrödinger
equation, white noise dispersion, geometric integration, quadratic first integral.