{
  "id": "1606.03039",
  "version": "v1",
  "published": "2016-06-09T17:53:50.000Z",
  "updated": "2016-06-09T17:53:50.000Z",
  "title": "Numerical validation of blow-up solutions for ODEs",
  "authors": [
    "Akitoshi Takayasu",
    "Kaname Matsue",
    "Takiko Sasaki",
    "Kazuaki Tanaka",
    "Makoto Mizuguchi",
    "Shin'ichi Oishi"
  ],
  "comment": "29 pages, 7 figures, 2 tables",
  "categories": [
    "math.NA",
    "math.DS"
  ],
  "abstract": "This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on compactifications and the Lyapunov function validation method. The necessary criteria for this construction can be verified using interval arithmetic techniques. Some numerical examples are presented to demonstrate the applicability of our method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-09T17:53:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C08",
      "35B44",
      "37B25",
      "65L99"
    ],
    "keywords": [
      "numerical validation",
      "lyapunov function validation method",
      "ordinary differential equations",
      "interval arithmetic techniques",
      "paper focuses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}