2021/02/28 by Shiyang Hu, Xin Wu, Enwei Liang · 13 citations
Mathematics · Physics and Astronomy · #Chaotic #Control theory (sociology) #Hamiltonian (control theory) #Hamiltonian system #Integrator #Lyapunov exponent #Model Reduction and Neural Networks #Nonlinear system #Numerical methods for differential equations #Parameter space #Phase space #Quantum chaos and dynamical systems #gr-qc
paper · pdf · doi:10.3847/1538-4365/abe69d
published in The Astrophysical Journal Supplement Series 253(2), 55 (Institute of Physics) · 27 pages, 14 figures
openalex created_date 2021/03/01 · openalex publication_date 2021/04/01 · arxiv created 2021/04/15 · arxiv updated 2021/04/16 · openalex updated_date 2026/08/05
Abstract In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable discretization-averaging of the Hamiltonian gradient, with a second-order accuracy to numerical solutions. A one-dimensional disordered discrete nonlinear Schrödinger equation and a post-Newtonian Hamiltonian system of spinning compact binaries are taken as our two examples. We demonstrate numerically that the proposed algorithm exhibits good long-term performance in the preservation of energy, if roundoff errors are neglected. This result is independent of time steps, initial orbital eccentricities, and regular and chaotic orbital dynamical behavior. In particular, the application of appropriately large time steps to the new algorithm is helpful in reducing time-consuming and roundoff errors. This new method, combined with fast Lyapunov indicators, is well suited to studying the influence of some parameters or initial conditions related to chaos in the two example problems. It is found that chaos in the former system is mainly responsible for one of the parameters. In the latter problem, a combination of small initial separations and high initial eccentricities can easily induce chaos.