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Mathematics > Numerical Analysis

arXiv:1807.11829 (math)
[Submitted on 31 Jul 2018 (v1), last revised 16 Aug 2018 (this version, v2)]

Title:Convergence of Lie group integrators

Authors:Charles Curry, Alexander Schmeding
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Abstract:We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.
Comments: 18 pages, uses TikZ, v2: corrected typos and minor errors, main results remain unchanged
Subjects: Numerical Analysis (math.NA); Differential Geometry (math.DG)
MSC classes: 65L20, 22F30, 53C30
Cite as: arXiv:1807.11829 [math.NA]
  (or arXiv:1807.11829v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1807.11829
Journal reference: Numerische Mathematik, 144(2), 357-373 (2020)
Related DOI: https://doi.org/10.1007/s00211-019-01083-1

Submission history

From: Alexander Schmeding [view email]
[v1] Tue, 31 Jul 2018 14:12:44 UTC (19 KB)
[v2] Thu, 16 Aug 2018 06:18:40 UTC (19 KB)
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