Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials
Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials
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DOI：
10.1007/s10543-021-00892-x
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发表时间：
2020-07
影响因子：
1.5
通讯作者：
A. Bazavov
中科院分区：
文献类型：
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作者：
A. Bazavov
基于显式经典Runge-Kutta格式，提出了一种新的无扰子李群方法。在这种格式中，指数在每个阶段都被重复使用，并且只需要存储两个量：在给定的Runge-Kutta阶段评估的微分方程的右侧和在同一阶段更新的函数值。该方案的下一阶段能够覆盖这些值。该结果在三阶段三阶方法中得到了证明，并提出了高阶方法的猜想。五个数值例子提供了支持的猜想。这类新的保结构积分器在数值求解流形上的微分方程方面有着广泛的应用。
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.