{
  "id": "1304.7016",
  "version": "v1",
  "published": "2013-04-25T20:08:34.000Z",
  "updated": "2013-04-25T20:08:34.000Z",
  "title": "Lie groups and numerical solutions of differential equations: Invariant discretization versus differential approximation",
  "authors": [
    "Decio Levi",
    "Pavel Winternitz"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the \"first differential approximation\" is invariant under the same Lie group as the original ordinary differential equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-25T20:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical solution",
      "invariant discretization",
      "original ordinary differential equation",
      "applying lie group theory",
      "first differential approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7016L"
    }
  }
}