https://doi.org/10.1140/epjp/s13360-026-07452-8
Regular Article
Explicit symplectic methods for nonseparable post-Newtonian Hamiltonian systems
1
School of Mathematics, Yunnan Normal University, 650500, Kunming, China
2
Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Yunnan Normal University, 650500, Kunming, China
a
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Received:
27
June
2025
Accepted:
17
February
2026
Published online:
2
March
2026
Abstract
Symplectic integrators proven to be highly effective for the numerical simulation of Hamiltonian systems. However, since the post-Newtonian (PN) Hamiltonian is typically nonseparable, the conventional use of implicit symplectic methods for such systems suffers from low computational efficiency due to the iterative nature of implicit schemes. In this paper, by employing doubled phase space techniques along with specific projection strategies, we develop efficient explicit symplectic methods for PN Hamiltonians. In particular, the proposed explicit symplectic methods, based on a special Hamiltonian splitting, take the advantage of the small PN parameter, yielding smaller truncation errors compared to the universally designed explicit symplectic methods provided that the PN parameter is sufficiently small. Finally, we present numerical comparisons between the proposed explicit methods and existing implicit symplectic methods for the 2PN Hamiltonian system of spinning compact binaries. The numerical results demonstrate the excellent long-term behavior, strong energy conservation, and high efficiency of the proposed explicit symplectic methods.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
