Year: 2022
Author: Yao-Lin Jiang, Zhen Miao, Yi Lu
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 4 : pp. 649–666
Abstract
In this paper, we derive and analyse waveform relaxation (WR) methods for solving differential equations evolving on a Lie-group. We present both continuous-time and discrete-time WR methods and study their convergence properties. In the discrete-time case, the novel methods are constructed by combining WR methods with Runge-Kutta-Munthe-Kaas (RK-MK) methods. The obtained methods have both advantages of WR methods and RK-MK methods, which simplify the computation by decoupling strategy and preserve the numerical solution of Lie-group equations on a manifold. Three numerical experiments are given to illustrate the feasibility of the new WR methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2101-m2020-0214
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 4 : pp. 649–666
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Lie-group equations Waveform relaxation RK-MK methods Convergence analysis.