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Linear energy-preserving integrators for Poisson systems

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Abstract

For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge–Kutta method with infinitely many stages.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Basel, 4051, Basel, Switzerland

    David Cohen

  2. Section de Mathématiques, Université de Genève, 1211, Genève 4, Switzerland

    Ernst Hairer

Authors
  1. David Cohen
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  2. Ernst Hairer
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Corresponding author

Correspondence to Ernst Hairer.

Additional information

Communicated by Christian Lubich.

This work was partially supported by the Fonds National Suisse, project No. 200020-126638.

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Cohen, D., Hairer, E. Linear energy-preserving integrators for Poisson systems. Bit Numer Math 51, 91–101 (2011). https://doi.org/10.1007/s10543-011-0310-z

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  • DOI: https://doi.org/10.1007/s10543-011-0310-z

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