{
  "id": "2011.07725",
  "version": "v1",
  "published": "2020-11-13T10:33:49.000Z",
  "updated": "2020-11-13T10:33:49.000Z",
  "title": "Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method",
  "authors": [
    "Riccardo Fazio"
  ],
  "comment": "28 pages, 7 figures and 4 tables. arXiv admin note: substantial text overlap with arXiv:2003.07971, arXiv:1212.5057",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-13T10:33:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65L10",
      "65L08",
      "34B15"
    ],
    "keywords": [
      "iterative transformation method",
      "semi-infinite intervals",
      "uniqueness",
      "boundary value problems",
      "problems seldom admit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}