1. Reliability of Lyapunov characteristic exponents computed by the two-particle method.
- Author
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Mei, Lijie and Huang, Li
- Subjects
- *
LYAPUNOV exponents , *DIFFERENTIAL equations , *MECHANICS (Physics) , *MONTE Carlo method , *COMPUTER simulation - Abstract
For highly complex problems, such as the post-Newtonian formulation of compact binaries, the two-particle method may be a better, or even the only, choice to compute the Lyapunov characteristic exponent (LCE). This method avoids the complex calculations of variational equations compared with the variational method. However, the two-particle method sometimes provides spurious estimates to LCEs. In this paper, we first analyze the equivalence in the definition of LCE between the variational and two-particle methods for Hamiltonian systems. Then, we develop a criterion to determine the reliability of LCEs computed by the two-particle method by considering the magnitude of the initial tangent (or separation) vector ξ 0 (or δ 0 ), renormalization time interval τ , machine precision ε , and global truncation error ϵ T . The reliable Lyapunov characteristic indicators estimated by the two-particle method form a V-shaped region, which is restricted by d 0 , ε , and ϵ T . Finally, the numerical experiments with the Hénon–Heiles system, the spinning compact binaries, and the post-Newtonian circular restricted three-body problem strongly support the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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