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.

翻译：根据明确的古典龙格-库塔方案,提出了无通勤者Liet组群方法的新格式。在这个格式中,每个阶段都重新使用指数,只需要储存两个数量:在给定的龙格-库塔阶段评价的差异方程的右手侧,以及在同一阶段更新的功能值。方案的下一个阶段能够覆盖这些值。3阶段的第三顺序方法证明了这一结果,并提出了更高顺序方法的推测。提供了五个数字例子以支持该预测。这个新的结构保护方程式类别在数字解析方程式上有着各种各样的应用。