Partitioned Runge--Kutta methods in Lie-group setting
Kenth Engų
Reports in Informatics No. 202, September 2000, Department of
Informatics, University of Bergen, Norway.
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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