• Numerical simulations for the...

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

Title:
Numerical simulations for the Toda lattices Hamiltonian system: Higher order symplectic illustrative perspective.
Authors:
Mushtaq A; Seksjon for matematikk, FLU, Nord Universitet, N-8049 Bodø, Norway., Noreen A; Seksjon for matematikk, FLU, Nord Universitet, N-8049 Bodø, Norway., Farooq MA; Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan.
Source:
PloS one [PLoS One] 2019 Apr 18; Vol. 14 (4), pp. e0215054. Date of Electronic Publication: 2019 Apr 18 (Print Publication: 2019).
Publication Type:
Journal Article; Research Support, Non-U.S. Gov't
Language:
English
Journal Info:
Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet ISSN: 1932-6203 (Electronic) Linking ISSN: 19326203 NLM ISO Abbreviation: PLoS One Subsets: MEDLINE
Imprint Name(s):
Original Publication: San Francisco, CA : Public Library of Science
MeSH Terms:
Algorithms* , Computer Simulation* , Models, Theoretical* , Numerical Analysis, Computer-Assisted*, Nonlinear Dynamics
Molecular Sequence:
figshare 10.6084/m9.figshare.7762775
Entry Date(s):
Date Created: 20190419 Date Completed: 20191227 Latest Revision: 20191227
Update Code:
20250114
PubMed Central ID:
PMC6472940
DOI:
10.1371/journal.pone.0215054
PMID:
30998691
Database:
MEDLINE

Weitere Informationen

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).

The authors have declared that no competing interests exist.