{
  "id": "2011.09889",
  "version": "v1",
  "published": "2020-11-19T15:23:19.000Z",
  "updated": "2020-11-19T15:23:19.000Z",
  "title": "Dynamically Consistent Approximate Rational Solutions to the Thomas-Fermi Equation",
  "authors": [
    "Ronald E. Mickens",
    "Isom H. Herron"
  ],
  "comment": "10 pages, 2 figures",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the predicted numerical values of the two approximate solutions, we compare these values with an accurate numerical solution obtained using a fourth-order Runge-Kutta method. We also present several new integral relations satisfied by the bounded solutions of the TF equation",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-19T15:23:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A45",
      "34B40",
      "34E05",
      "41A20",
      "81V45"
    ],
    "keywords": [
      "dynamically consistent approximate rational solutions",
      "thomas-fermi equation",
      "rational approximate solutions",
      "nonlinear differential equation",
      "fourth-order runge-kutta method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}