Casimir preserving stochastic Lie–Poisson integrators

IF 3.1 3区数学 Q1 MATHEMATICS

Advances in Difference Equations Pub Date : 2024-01-02 DOI:10.1186/s13662-023-03796-y

Erwin Luesink, Sagy Ephrati, Paolo Cifani, Bernard Geurts

引用次数: 0

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 using 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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卡西米尔保全随机李-泊松积分器

通过扩展 Runge-Kutta Munthe-Kaas 方法，为具有 Stratonovich 噪声的随机 Lie-Poisson 方程开发了卡西米尔保留积分器。沿随机轨迹保留了基本的列-泊松结构。推导出了一个相关的列代数随机微分方程。该微分方程的解使用指数图更新了Lie-Poisson动力学的演化。所构建的数值方法精确地保留了卡西米尔不变式，这对长时间积分非常重要。这一点在随机重顶和随机正弦-欧拉方程中得到了数值说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

8.60

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.