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Casimir preserving stochastic Lie-Poisson integrators
- Publication Year :
- 2021
-
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.<br />Comment: 27 pages, 9 figures, fifth version, all comments are welcome!
- Subjects :
- Mathematics - Numerical Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.13143
- Document Type :
- Working Paper