A new class of G(ϵ)-symplectic general linear methods

Michal Braś, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review


A new class of G(ϵ)-symplectic general linear methods for numerical integration of Hamiltonian systems of differential equations is described. Order conditions for these methods are derived using Albrecht approach and the construction of G(ϵ)-symplectic method is described based on solving minimization problems with nonlinear inequality constrains. Examples of methods up to the order four are presented. Numerical experiments confirm that these methods achieve the expected order of accuracy and that they approximately preserve Hamiltonians of differential systems.

Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalApplied Numerical Mathematics
StatePublished - Jan 2023


  • Construction of methods
  • G(ϵ)-symplecticness
  • General linear methods
  • Order conditions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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