{
  "id": "1411.7117",
  "version": "v1",
  "published": "2014-11-26T06:32:11.000Z",
  "updated": "2014-11-26T06:32:11.000Z",
  "title": "Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations",
  "authors": [
    "Jacky Cresson",
    "Frédéric Pierret"
  ],
  "categories": [
    "math.NA",
    "math.CT"
  ],
  "abstract": "We define an abstract framework called {\\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit three main discrete associate : the differential, integral or variational discrete embeddings which corresponds to classical numerical scheme including variational integrators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-26T06:32:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ordinary differential equations",
      "discrete structures",
      "variational discrete embeddings",
      "formal functional relations",
      "main discrete associate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.7117C"
    }
  }
}