Multirevolution integrators for differential equations with fast stochastic oscillations
We introduce new integrators for highly oscillatory stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise.
The approach is based on the framework of multi-revolution composition methods previously introduced for deterministic and stochastic problems and it inherits its geometric features, in particular to design integrators preserving exactly quadratic first integrals. Applications include highly-oscillatory Kubo oscillators and spatial discretizations of the nonlinear Schrödinger equation with fast white noise dispersion.
Joint work with Adrien Laurent.
Preprints available at http://www.unige.ch/~vilmart