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 pr...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-KuttaMunthe-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.展开更多
基金supported by the Natural Science Foundation of China(NSFC)under grant 11871393International Science and Technology Cooperation Program of Shaanxi Key Research&Development Plan under grant 2019KWZ-08.
文摘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-KuttaMunthe-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.
