{
  "id": "1612.08803",
  "version": "v1",
  "published": "2016-12-28T04:50:49.000Z",
  "updated": "2016-12-28T04:50:49.000Z",
  "title": "A Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations",
  "authors": [
    "Vladislav V. Kravchenko",
    "Sergii M. Torba"
  ],
  "categories": [
    "math.CA",
    "math.NA"
  ],
  "abstract": "A Neumann series of Bessel functions (NSBF) representation for solutions of Sturm-Liouville equations and for their derivatives is obtained. The representation possesses an attractive feature for applications: for all real values of the spectral parameter $\\omega$ the difference between the exact solution and the approximate one (the truncated NSBF) depends on $N$ (the truncation parameter) and the coefficients of the equation and does not depend on $\\omega$. A similar result is valid when $\\omega\\in\\mathbb{C}$ belongs to a strip $|Im\\omega|<C$. This feature makes the NSBF representation especially useful for applications requiring computation of solutions for large intervals of $\\omega$. Error and decay rate estimates are obtained. An algorithm for solving initial value, boundary value or spectral problems for the Sturm-Liouville equation is developed and illustrated on a test problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-28T04:50:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A25",
      "34A45",
      "34B05",
      "34B24",
      "41A10",
      "41A25",
      "42C10",
      "65L05",
      "65L15"
    ],
    "keywords": [
      "bessel functions representation",
      "sturm-liouville equation",
      "neumann series",
      "decay rate estimates",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}