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Volume 40, Issue 4
Waveform Relaxation Methods for Lie-Group Equations

Yao-Lin Jiang, Zhen Miao & Yi Lu

DOI: 10.4208/jcm.2101-m2020-0214

J. Comp. Math., 40 (2022), pp. 649-666.

Published online: 2022-04

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  • 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.

  • Keywords

Lie-group equations, Waveform relaxation, RK-MK methods, Convergence analysis.

  • AMS Subject Headings

65L05, 65L06, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yljiang@mail.xjtu.edu.cn (Yao-Lin Jiang)

mz91127@126.com (Zhen Miao)

luyi06@gmail.com (Yi Lu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-649, author = {Jiang , Yao-LinMiao , Zhen and Lu , Yi}, title = {Waveform Relaxation Methods for Lie-Group Equations}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2101-m2020-0214}, url = {http://global-sci.org/intro/article_detail/jcm/20505.html} }
TY - JOUR T1 - Waveform Relaxation Methods for Lie-Group Equations AU - Jiang , Yao-Lin AU - Miao , Zhen AU - Lu , Yi JO - Journal of Computational Mathematics VL - 4 SP - 649 EP - 666 PY - 2022 DA - 2022/04 SN - 40 DO - http://doi.org/10.4208/jcm.2101-m2020-0214 UR - https://global-sci.org/intro/article_detail/jcm/20505.html KW - Lie-group equations, Waveform relaxation, RK-MK methods, Convergence analysis. AB -

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.

Yao-Lin Jiang, Zhen Miao & Yi Lu. (2022). Waveform Relaxation Methods for Lie-Group Equations. Journal of Computational Mathematics. 40 (4). 649-666. doi:10.4208/jcm.2101-m2020-0214
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