Multirevolution integrators for differential equations with fast stochastic oscillations
Numerical Analysis
2020-02-04 v2 Numerical Analysis
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.
Cite
@article{arxiv.1902.01716,
title = {Multirevolution integrators for differential equations with fast stochastic oscillations},
author = {Adrien Laurent and Gilles Vilmart},
journal= {arXiv preprint arXiv:1902.01716},
year = {2020}
}
Comments
27 pages