{
  "id": "2004.00424",
  "version": "v1",
  "published": "2020-03-29T20:57:57.000Z",
  "updated": "2020-03-29T20:57:57.000Z",
  "title": "Solving the inverse problem for an ordinary differential equation using conjugation",
  "authors": [
    "Alfaro Vigo",
    "D. G",
    "Alvarez",
    "A. C",
    "Chapiro",
    "G.",
    "Garcia-Mokina",
    "G.",
    "Moreira",
    "C. G. T. A"
  ],
  "categories": [
    "math.OC",
    "cs.NA",
    "math.DS",
    "math.NA",
    "nlin.CD"
  ],
  "abstract": "We consider the following inverse problem for an ordinary differential equations (ODE): given a set of data points $(t_i,x_i)$, $i=1,\\cdots,N$, find an ODE $x^\\prime(t) = v (x(t))$ that admits a solution $x(t)$ such that $x_i = x(t_i)$. To determine the field $v(x)$, we use the conjugate map defined by Schr\\\"{o}der equation and the solution of a related Julia equation. We also study existence, uniqueness, stability and other properties of this solution. Finally, we present several numerical methods for the approximation of the field $v(x)$ and provide some illustrative examples of the application of these methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-29T20:57:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65Y04",
      "G.1.2"
    ],
    "keywords": [
      "ordinary differential equation",
      "inverse problem",
      "conjugation",
      "study existence",
      "data points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}