论文标题
不含换向器的谎言组方法，具有最低存储要求和重复使用指数
Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials
论文作者
论文摘要
基于明确的经典runge-kutta方案，提出了针对无通勤谎言组方法的新格式。在此格式中，每个阶段都重复使用指数，并且仅需要两个数量的存储：在给定的runge-kutta阶段评估的微分方程的右侧侧侧以及在同一阶段更新的函数值。该方案的下一个阶段能够覆盖这些值。结果已被证明是三阶三阶方法的证明，并制定了高阶方法的猜想。提供了五个数值示例以支持猜想。这类新型结构的集成器具有多种应用程序，用于在流形上求解微分方程。
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.
