{
  "id": "1306.2914",
  "version": "v3",
  "published": "2013-06-12T18:13:26.000Z",
  "updated": "2014-04-29T00:26:22.000Z",
  "title": "Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems",
  "authors": [
    "Vladislav V. Kravchenko",
    "Sergii M. Torba"
  ],
  "comment": "32 pages, 9 figures, 4 tables; Sections 6 and 7 extended, runtimes added",
  "categories": [
    "math.CA",
    "math-ph",
    "math.FA",
    "math.MP",
    "math.NA"
  ],
  "abstract": "A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues is reduced to approximation of a primitive of the potential by a finite linear combination of generalized wave polynomials introduced in arXiv:1208.5984, arXiv:1208.6166. The method allows one to compute both lower and higher eigendata with an extreme accuracy.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-29T00:26:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A45",
      "34B09",
      "34B24",
      "34E05",
      "34L16",
      "34L40",
      "41A30",
      "41A50",
      "41A55",
      "65D30",
      "65L05",
      "65L15",
      "65L99",
      "81Q05"
    ],
    "keywords": [
      "highly accurate solution",
      "spectral problems",
      "analytic approximation",
      "applications",
      "finite linear combination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2914K"
    }
  }
}