Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems  

作　　者：Zhen Miao Bin Wang Yaolin Jiang 

机构地区：[1]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710072,P.R.China [2]School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an 710049,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期121-144,共24页高等学校计算数学学报（英文版）

基　　金：supported by the NSFC(Grants 12371403,12271426);by the Key Research and Development Projects of Shaanxi Province(Grant 2023-YBSF-399).

摘　　要：In this paper,we formulate and analyse a kind of parareal-RKN algo-rithms with energy conservation for Hamiltonian systems.The proposed algorithms are constructed by using the ideas of parareal methods,Runge-Kutta-Nystrom(RKN)methods and projection methods.It is shown that the algorithms can exactly pre-serve the energy of Hamiltonian systems.Moreover,the convergence of the integra-tors is rigorously analysed.Three numerical experiments are carried out to support the theoretical results presented in this paper and show the numerical behaviour of the derived algorithms.

关 键 词：Parareal methods Runge-Kutta-Nystrom methods Hamiltonian systems energy conservation 

分 类 号：O24[理学—计算数学]