Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials
arXiv:2007.04225 · doi:10.1007/s10543-021-00892-x
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.
41 pages, 10 figures. Minor revisions to bring the preprint in line with the final published version. The published version is slightly shortened in the introductory part