Casimir preserving stochastic Lie-Poisson integrators
Numerical Analysis
2023-07-19 v6 Numerical Analysis
Abstract
Casimir preserving integrators for stochastic Lie-Poisson equations with Stratonovich noise are developed extending Runge-Kutta Munthe-Kaas methods. The underlying Lie-Poisson structure is preserved along stochastic trajectories. A related stochastic differential equation on the Lie algebra is derived. The solution of this differential equation updates the evolution of the Lie-Poisson dynamics by means of the exponential map. The constructed numerical method conserves Casimir-invariants exactly, which is important for long time integration. This is illustrated numerically for the case of the stochastic heavy top and the stochastic sine-Euler equations.
Keywords
Cite
@article{arxiv.2111.13143,
title = {Casimir preserving stochastic Lie-Poisson integrators},
author = {Erwin Luesink and Sagy Ephrati and Paolo Cifani and Bernard Geurts},
journal= {arXiv preprint arXiv:2111.13143},
year = {2023}
}
Comments
27 pages, 9 figures, fifth version, all comments are welcome!