Foundations of Computational Mathematics

, Volume 10, Issue 6, pp 673–693

Energy-Preserving Integrators and the Structure of B-series

  • Elena Celledoni
  • Robert I. McLachlan
  • Brynjulf Owren
  • G. R. W. Quispel


B-series are a powerful tool in the analysis of Runge–Kutta numerical integrators and some of their generalizations (“B-series methods”). A general goal is to understand what structure-preservation can be achieved with B-series and to design practical numerical methods that preserve such structures. B-series of Hamiltonian vector fields have a rich algebraic structure that arises naturally in the study of symplectic or energy-preserving B-series methods and is developed in detail here. We study the linear subspaces of energy-preserving and Hamiltonian modified vector fields which admit a B-series, their finite-dimensional truncations, and their annihilators. We characterize the manifolds of B-series that are conjugate to Hamiltonian and conjugate to energy-preserving and describe the relationships of all these spaces.


B-series methods Symplectic integration Energy preservation Trees Conjugate methods 

Mathematics Subject Classification (2000)

65P10 65D30 05C05 37M15 


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Copyright information

© SFoCM 2010

Authors and Affiliations

  • Elena Celledoni
    • 1
  • Robert I. McLachlan
    • 2
  • Brynjulf Owren
    • 1
  • G. R. W. Quispel
    • 3
  1. 1.Department of Mathematical SciencesNTNUTrondheimNorway
  2. 2.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand
  3. 3.Mathematics DepartmentLa Trobe UniversityVICAustralia

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