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A new format for commutator-free Lie group methods is proposed based onexplicit classical Runge-Kutta schemes. In this format exponentials are reusedat every stage and the storage is required only for two quantities: the righthand side of the differential equation evaluated at a given Runge-Kutta stageand the function value updated at the same stage. The next stage of the schemeis able to overwrite these values. The result is proven for a 3-stage thirdorder method and a conjecture for higher order methods is formulated. Fivenumerical examples are provided in support of the conjecture. This new class ofstructure-preserving integrators has a wide variety of applications fornumerically solving differential equations on manifolds.

Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials