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arXiv · 2007.04225

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

Alexei Bazavov
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Abstract

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.

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Alexei Bazavov. 2021-09-08. Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials. https://doi.org/10.1007/s10543-021-00892-x

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