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Numerische Mathematik

, Volume 103, Issue 4, pp 575–590 | Cite as

An Algebraic Approach to Invariant Preserving Integators: The Case of Quadratic and Hamiltonian Invariants

  • Philippe ChartierEmail author
  • Erwan Faou
  • Ander Murua
Original article

Abstract

In this article, conditions for the preservation of quadratic and Hamiltonian invariants by numerical methods which can be written as B-series are derived in a purely algebraical way. The existence of a modified invariant is also investigated and turns out to be equivalent, up to a conjugation, to the preservation of the exact invariant. A striking corollary is that a symplectic method is formally conjugate to a method that preserves the Hamitonian exactly. Another surprising consequence is that the underlying one-step method of a symmetric multistep scheme is formally conjugate to a symplectic P-series when applied to Newton’s equations of motion.

Keywords

Hamiltonian System Hopf Algebra Rooted Tree Hamiltonian Function Algebraic Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.IPSOINRIARennesFrance
  2. 2.Konputazio Zientziak eta A. A. saila, Informatika FakultateaUniversity of the Basque CountryDonostia/San SebastiànSpain

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