{
  "id": "1612.02417",
  "version": "v1",
  "published": "2016-12-07T20:52:37.000Z",
  "updated": "2016-12-07T20:52:37.000Z",
  "title": "Conservative methods for dynamical systems",
  "authors": [
    "Andy T. S. Wan",
    "Alexander Bihlo",
    "Jean-Christophe Nave"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and non-autonomous dynamical systems with conserved quantities of arbitrary forms, such as time-dependent conserved quantities. Sufficient conditions to construct conservative schemes of arbitrary order are derived using the multiplier method. General formulas for first-order conservative schemes are constructed using divided difference calculus. New conservative schemes are found for various dynamical systems such as Euler's equation of rigid body rotation, Lotka-Volterra systems, the planar restricted three-body problem and the damped harmonic oscillator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-07T20:52:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65L05",
      "65L06",
      "65L12",
      "65L20",
      "65P10",
      "65Z05",
      "37M05",
      "37M15"
    ],
    "keywords": [
      "dynamical systems",
      "conservative methods",
      "conservative schemes",
      "conserved quantities",
      "construct conservative finite difference schemes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}