Cost Efficient Lie Group Integrators in the RKMK Class

Authors: Casas F.1; Owren B.2

Source: Bit Numerical Mathematics, Volume 43, Number 4, December 2003 , pp. 723-742(20)

Publisher: Springer

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Abstract:

In this work a systematic procedure is implemented in order to minimise the computational cost of the Runge–Kutta–Munthe-Kaas (RKMK) class of Lie-group solvers. The process consists of the application of a linear transformation to the stages of the method and the analysis of a graded free Lie algebra to reduce the number of commutators involved. We consider here RKMK integration methods up to order seven based on some of the most popular Runge–Kutta schemes.

Keywords: time integration; geometric integration; numerical integration of ordinary differential equ; numerical analysis; Lie algebras; Lie groups

Document Type: Research article

DOI: 10.1023/B:BITN.0000009959.29287.d4

Affiliations: 1: Departament de Matemàtiques, Universitat Jaume I, 12071-Castellón, Spain., Email: Fernando.Casas@uji.es 2: Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway, and Center for Advanced Study, Drammensveien 78, 0271 Oslo, Norway., Email: Brynjulf.Owren@math.ntnu.no

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