The control of parasitism in $G$-symplectic methods

John C. Butcher, Yousaf Habib, Adrian T. Hill, Terence J T Norton

Research output: Contribution to journalArticle

14 Citations (Scopus)
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Abstract

G-symplectic general linear methods are designed to approximately preserve symplectic invariants for Hamiltonian systems. In this paper, the properties of G-symplectic methods are explored computationally and theoretically. Good preservation properties are observed over long times for many parameter ranges, but, for other parameter values, the parasitic behavior, to which multivalue methods are prone, corrupts the numerical solution by the growth of small perturbations. Two approaches for alleviating this effect are considered. First, compositions of methods with growth parameters of opposite signs can be used to cancel the long-term effect of parasitism. Second, methods can be constructed for which the growth parameters are zero by design. Each of these remedies is found to be successful in eliminating parasitic behavior in long-term simulations using a variety of test problems.

Original languageEnglish
Pages (from-to)2440-2465
Number of pages26
JournalSIAM Journal on Numerical Analysis (SINUM)
Volume52
Issue number5
Early online date14 Oct 2014
DOIs
Publication statusE-pub ahead of print - 14 Oct 2014

Fingerprint

Symplectic Methods
Hamiltonians
General Linear Methods
Cancel
Small Perturbations
Preservation
Test Problems
Hamiltonian Systems
Numerical Solution
Chemical analysis
Invariant
Zero
Range of data
Simulation

Keywords

  • General linear methods
  • Parasitism
  • Symplectic

Cite this

The control of parasitism in $G$-symplectic methods. / Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J T.

In: SIAM Journal on Numerical Analysis (SINUM), Vol. 52, No. 5, 14.10.2014, p. 2440-2465.

Research output: Contribution to journalArticle

Butcher, John C. ; Habib, Yousaf ; Hill, Adrian T. ; Norton, Terence J T. / The control of parasitism in $G$-symplectic methods. In: SIAM Journal on Numerical Analysis (SINUM). 2014 ; Vol. 52, No. 5. pp. 2440-2465.
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