Casimir preserving stochastic Lie-Poisson integrators

Erwin Luesink; Sagy Ephrati; Paolo Cifani; Bernard Geurts

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arXiv · 2111.13143

Casimir preserving stochastic Lie-Poisson integrators

Erwin Luesink·Sagy Ephrati·Paolo Cifani·Bernard Geurts

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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.

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Erwin Luesink, Sagy Ephrati, Paolo Cifani, Bernard Geurts. 2021-11-25. Casimir preserving stochastic Lie-Poisson integrators. https://arxiv.org/abs/2111.13143

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