{
  "id": "1002.1387",
  "version": "v1",
  "published": "2010-02-08T17:32:25.000Z",
  "updated": "2010-02-08T17:32:25.000Z",
  "title": "Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their blended implementation",
  "authors": [
    "Luigi Brugnano",
    "Felice Iavernaro",
    "Donato Trigiante"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. Recently, a new class of methods, named \"Hamiltonian Boundary Value Methods (HBVMs)\" has been introduced and analysed, which are able to exactly preserve polynomial Hamiltonians of arbitrarily high degree. We here study a further property of such methods, namely that of having, when cast as Runge-Kutta methods, a matrix of the Butcher tableau with the same spectrum (apart the zero eigenvalues) as that of the corresponding Gauss-Legendre method, independently of the considered abscissae. Consequently, HBVMs are always perfectly A-stable methods. Moreover, this allows their efficient \"blended\" implementation, for solving the generated discrete problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-08T17:32:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65P10",
      "65L05",
      "65L06",
      "65L80",
      "65H10"
    ],
    "keywords": [
      "hamiltonian boundary value methods",
      "isospectral property",
      "blended implementation",
      "integrating autonomous hamiltonian systems",
      "exactly preserve polynomial hamiltonians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.1387B"
    }
  }
}