TY - JOUR
T1 - Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems
AU - Miao , Zhen
AU - Wang , Bin
AU - Jiang , Yaolin
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 121
EP - 144
PY - 2024
DA - 2024/02
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0081
UR - https://global-sci.org/intro/article_detail/nmtma/22913.html
KW - Parareal methods, Runge-Kutta-Nyström methods, Hamiltonian systems, energy conservation.
AB - <p style="text-align: justify;">In this paper, we formulate and analyse a kind of parareal-RKN algorithms with energy conservation for Hamiltonian systems. The proposed algorithms
are constructed by using the ideas of parareal methods, Runge-Kutta-Nyström (RKN)
methods and projection methods. It is shown that the algorithms can exactly preserve the energy of Hamiltonian systems. Moreover, the convergence of the integrators 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.</p>