Abstract
We introduce partitioned Runge–Kutta (PRK) methods as geometric integrators in the Runge–Kutta–Munthe-Kaas (RKMK) method hierarchy. This is done by first noticing that tangent and cotangent bundles are the natural domains for the differential equations to be solved. Next, we equip the (co)tangent bundle of a Lie group with a group structure and treat it as a Lie group. The structure of the differential equations on the (co)tangent-bundle Lie group is such that partitioned versions of the RKMK methods are naturally introduced. Numerical examples are included to illustrate the new methods.
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Engø, K. Partitioned Runge–Kutta Methods in Lie-Group Setting. BIT Numerical Mathematics 43, 21–39 (2003). https://doi.org/10.1023/A:1023668015087
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DOI: https://doi.org/10.1023/A:1023668015087