Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems

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.