English

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.

Keywords

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

R2 v1 2026-06-23T07:32:33.133Z