{
  "id": "1304.0673",
  "version": "v1",
  "published": "2013-04-02T15:55:28.000Z",
  "updated": "2013-04-02T15:55:28.000Z",
  "title": "On an asymptotic method for computing the modified energy for symplectic methods",
  "authors": [
    "Per Christian Moan",
    "Jitse Niesen"
  ],
  "comment": "16 pages, 7 figures",
  "journal": "Discrete Contin. Dyn. Syst. 34 (2014) 1105-1120",
  "doi": "10.3934/dcds.2014.34.1105",
  "categories": [
    "math.NA"
  ],
  "abstract": "We revisit an algorithm by Skeel et al. for computing the modified, or shadow, energy associated with the symplectic discretization of Hamiltonian systems. By rephrasing the algorithm as a Richardson extrapolation scheme arbitrary high order of accuracy is obtained, and provided error estimates show that it does capture the theoretical exponentially small drift associated with such discretizations. Several numerical examples illustrate the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-02T15:55:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65P10",
      "37J40",
      "37M15"
    ],
    "keywords": [
      "symplectic methods",
      "asymptotic method",
      "modified energy",
      "extrapolation scheme arbitrary high order",
      "exponentially small drift"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0673M"
    }
  }
}