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PLoS One. 2019 Apr 18;14(4):e0215054. doi: 10.1371/journal.pone.0215054. eCollection 2019.

Numerical simulations for the Toda lattices Hamiltonian system: Higher order symplectic illustrative perspective.

Author information

Seksjon for matematikk, FLU, Nord Universitet, N-8049 Bodø, Norway.
Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan.


In this paper we apply some higher order symplectic numerical methods to analyze the dynamics of 3-site Toda lattices (reduced to relative coordinates). We present benchmark numerical simulations that has been generated from the HOMsPY (Higher Order Methods in Python) library. These results provide detailed information of the underlying Hamiltonian system. These numerical simulations reinforce the claim that the symplectic numerical methods are highly accurate qualitatively and quantitatively when applied not only to Hamiltonian of the Toda lattices, but also to other physical models. Excepting exactly integrable models, these symplectic numerical schemes are superior, efficient, energy preserving and suitable for a long time integrations, unlike standard non-symplectic numerical methods which lacks preservation of energy (and other constants of motion, when such exist).

Conflict of interest statement

The authors have declared that no competing interests exist.

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