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Lie-group methods

Abstract : Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively-correct geometry and dynamics and in the minimisation of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.
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https://hal.archives-ouvertes.fr/hal-01328729
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Submitted on : Wednesday, June 8, 2016 - 1:51:01 PM
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Arieh Iserles, Hans Munthe-Kaas, Syvert Nørsett, Antonella Zanna. Lie-group methods. Acta Numerica, Cambridge University Press (CUP), 2005, ⟨10.1017/S0962492900002154⟩. ⟨hal-01328729⟩

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