Generalized flow-composed symplectic methodsfor post-Newtonian Hamiltonian systems

• Published in: Journal of cosmology and astroparticle physics Vol. 2024; no. 10; p. 022
• Main Authors: Huang, Shixiang, Zeng, Kaiming, Niu, Xinghua, Lijie Mei
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.10.2024
• Subjects: Hamiltonian functions; Runge-Kutta method
• ISSN: 1475-7516; 1475-7516
• DOI: 10.1088/1475-7516/2024/10/022

Due to the nonseparability of the post-Newtonian (PN) Hamiltonian systems of compactobjects, the symplectic methods that admit the linear error growth and the near preservation offirst integrals are always implicit as explicit symplectic methods have not been currently foundfor general nonseparable Hamiltonian systems. Since the PN Hamiltonian has a particularformulation that includes a dominant Newtonian part and a perturbation PN part, we present thegeneralized flow-composed Runge-Kutta (GFCRK) method with a free parameter λ to PNHamiltonian systems. It is shown that the GFCRK method is symplectic once the underlying RK methodis symplectic, and it is symmetric once the underlying RK method is symmetric under the settingλ = 1/2. Numerical experiments with the 2PN Hamiltonian of spinning compact binariesdemonstrate the higher accuracy and efficiency of the symplectic GFCRK method than the underlyingsymplectic RK method in the case of weak PN effect. Meanwhile, the numerical results also supporthigher efficiency of the symplectic GFCRK method than the semi-explicit mixed symplectic method ofthe same order.