@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} }