Construction of G- or G(ϵ)-symplectic general linear methods

Michal Braś, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

Abstract

We describe the construction of G- or G(ϵ)-symplectic, and parasitism free or ϵ-parasitism free general linear methods for numerical integration of Hamiltonian systems of differential equations. Examples of such methods are presented up to the order p=4 and stage order q=p−1. Numerical experiments confirm that all methods achieve the expected order of accuracy, and that these methods approximately preserve Hamiltonians as well as quadratic invariants of differential systems.

Original languageEnglish (US)
Article number127204
JournalApplied Mathematics and Computation
Volume431
DOIs
StatePublished - Oct 15 2022

Keywords

  • Construction of methods
  • G-symplecticness
  • General linear methods
  • Order conditions
  • Parasitism

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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