{
  "id": "2210.09274",
  "version": "v1",
  "published": "2022-10-17T17:27:02.000Z",
  "updated": "2022-10-17T17:27:02.000Z",
  "title": "Discretization of the wave equation on a metric graph",
  "authors": [
    "Sergei A. Avdonin",
    "Aleksander S. Mikhaylov",
    "Victor S. Mikhaylov",
    "Abdon E. Choque-Rivero"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous case is also drawn. As an example the problem of shape controllability from the boundary is studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-17T17:27:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35Q93",
      "93B05",
      "93C20",
      "37M15",
      "37J51"
    ],
    "keywords": [
      "wave equation",
      "metric graph",
      "discretization",
      "discrete graph",
      "discrete time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}