Efficient high-order explicit symplectic splitting methods for post-Newtonian Hamiltonian systems
Year: 2026
Type: preprint
Abstract: The nonseparability of post-Newtonian (PN) Hamiltonian systems typically necessitates the use of computationally expensive implicit integrators. Recent research overcomes this limitation by embedding the dynamics into a doubled phase space, which enables the development of explicit symplectic methods. However, existing specially designed explicit integrators suffer from order reduction for high-order methods when the time stepsize is small, i.e., $h <\varepsilon^3$. In this paper, we propose a novel extension and splitting approach for the doubled Hamiltonian, under which specially designed explicit symplectic integrators can be constructed. It is shown that the proposed integrators achieve genuine high-order convergence without order reduction and take advantage of the small PN parameter $\varepsilon$. Numerical results from simulations with 2PN spinning binaries demonstrate superior long-term conservation of invariants and significantly higher computational efficiency compared to both implicit methods and existing explicit splitting techniques.
Source: arXiv (Cornell University)
Authors: Jiang, Yujie, Mei, Lijie
Institution: Yunnan Normal University
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7879078830
OpenAlex ID: W7167236609
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