Krylov integrators for Hamiltonian systems

Research output: Contribution to journalArticleScientificpeer-review


  • Timo Eirola
  • Antti Koskela

Research units

  • University of Helsinki


We consider Arnoldi-like processes to obtain symplectic subspaces for Hamiltonian systems. Large dimensional systems are locally approximated by ones living in low dimensional subspaces, and we especially consider Krylov subspaces and some of their extensions. These subspaces can be utilized in two ways: by solving numerically local small dimensional systems and then mapping back to the large dimension, or by using them for the approximation of necessary functions in exponential integrators applied to large dimensional systems. In the former case one can expect an excellent energy preservation and in the latter this is so for linear systems. We consider second order exponential integrators which solve linear systems exactly and for which these two approaches are in a certain sense equivalent. We also consider the time symmetry preservation properties of the integrators. In numerical experiments these methods combined with symplectic subspaces show promising behavior also when applied to nonlinear Hamiltonian problems.


Original languageEnglish
Pages (from-to)57–76
JournalBIT Numerical Mathematics
Issue number1
Early online date1 Jan 2018
Publication statusPublished - Mar 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Exponential integrators, Hamiltonian Lanczos algorithm, Hamiltonian systems, Krylov subspace methods, Symmetric integrators, Symplectic integrators

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