具有最小存储需求并复用指数的无交换子李群方法
Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials
AI总结：
本文基于显式 Runge-Kutta 格式提出可复用指数、仅需两项存储的无交换子李群积分方法，证明三阶情形并以五个数值例子支持高阶猜想。
摘要：
本文基于显式经典 Runge-Kutta 格式，提出了一种用于无交换子李群方法的新形式。在该形式中，指数在每个阶段都被复用，并且只需为两个量提供存储：在给定 Runge-Kutta 阶段求值的微分方程右端项，以及在同一阶段更新的函数值。该格式的下一阶段能够覆盖这些值。对于一个三阶段三阶方法，本文证明了相应结果；并对更高阶方法给出了一个猜想。文中提供了五个数值例子以支持该猜想。这一新的保结构积分类在流形上微分方程的数值求解中具有广泛应用。
英文摘要：
A new format for commutator-free Lie group methods is proposed based on explicit classical Runge-Kutta schemes. In this format exponentials are reused at every stage and the storage is required only for two quantities: the right hand side of the differential equation evaluated at a given Runge-Kutta stage and the function value updated at the same stage. The next stage of the scheme is able to overwrite these values. The result is proven for a 3-stage third order method and a conjecture for higher order methods is formulated. Five numerical examples are provided in support of the conjecture. This new class of structure-preserving integrators has a wide variety of applications for numerically solving differential equations on manifolds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
