{
  "id": "1408.4029",
  "version": "v2",
  "published": "2014-08-18T14:59:51.000Z",
  "updated": "2014-08-22T18:35:14.000Z",
  "title": "Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations",
  "authors": [
    "D. Nazari Susahab",
    "S. Shahmorad"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-\\tau)^{\\alpha-1}$ with $0 <\\alpha <1.$ Convergence orders of the methods are determined and their superconvergence is also analyzed. The paper closes with numerical examples and application to fractional differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-18T14:59:51.000Z",
      "abstract": "We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-\\tau)^{\\alpha-1}$ with $0 <\\alpha <1.$ Convergence orders of the methods are determined and their superconvergence and linear stability properties are also analyzed. The paper closes with numerical examples and application to fractional differential equations.",
      "comment": "19 pages, 8 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-22T18:35:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65R20",
      "65L60",
      "34A08"
    ],
    "keywords": [
      "weakly singular volterra integral equations",
      "fractional differential equations",
      "multistep collocation methods",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4029N"
    }
  }
}