{
  "id": "1208.6410",
  "version": "v1",
  "published": "2012-08-31T07:26:10.000Z",
  "updated": "2012-08-31T07:26:10.000Z",
  "title": "Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation",
  "authors": [
    "Helge Holden",
    "Ujjwal Koley",
    "Nils Henrik Risebro"
  ],
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\\in H^3(\\R)$, the scheme is shown to converge to a classical solution, and if the regularity of the initial data is smaller, $u_0\\in L^2(\\R)$, then the scheme converges strongly in $L^2(0,T;L^2_{\\mathrm{loc}}(\\R))$ to a weak solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-31T07:26:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M12",
      "35Q20",
      "65M06"
    ],
    "keywords": [
      "fully discrete finite difference scheme",
      "korteweg-de vries equation",
      "convergence",
      "initial data",
      "scheme converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.6410H"
    }
  }
}