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 - <p style="text-align: justify;">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.</p>