Explicit symplectic algorithms for time-transformed Hamiltonians
type: Item
instance of: scholarly article
title: Explicit symplectic algorithms for time-transformed Hamiltonians
zbMATH Open document ID: 0949.70005
DOI: 10.1023/A:1008368322547
author: Seppo Mikkola
author: Kiyotaka Tanikawa
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2000-11-20T00:00:00Z
review text: The authors discuss a special time transformation, such that applied to a separated Hamiltonian, the transformed Hamiltonian is again separated and thus permits the use of explicit symplectic integrators. It is shown that the application of leapfrog algorithm to the time-transformed two-body motion yields the exact Keplerian ellipse; errors appear only in the integration of the time variable. After a discussion of \(N\)-body systems and the use of higher-order methods, the authors present results of some numerical experiments. They show that even collision orbits can be computed without catastrophic errors.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 70-08
Mathematics Subject Classification ID: 70F05
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1442301
zbMATH Keywords: numerical error
zbMATH Keywords: time-transformed Hamiltonians
zbMATH Keywords: time transformation
zbMATH Keywords: orbit calculation
zbMATH Keywords: explicit symplectic integrator
zbMATH Keywords: leapfrog algorithm
zbMATH Keywords: time-transformed two-body motion
zbMATH Keywords: exact Keplerian ellipse
zbMATH Keywords: \(N\)-body systems
zbMATH Keywords: higher-order methods
zbMATH Keywords: collision orbits
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1442301