{
  "id": "1707.01566",
  "version": "v1",
  "published": "2017-07-05T20:10:21.000Z",
  "updated": "2017-07-05T20:10:21.000Z",
  "title": "Numerical Methods for Fractional Diffusion",
  "authors": [
    "Andrea Bonito",
    "Juan Pablo Borthagaray",
    "Ricardo H. Nochetto",
    "Enrique Otarola",
    "Abner J. Salgado"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the extension to one higher dimension. The second method is the integral formulation and deals with singular non-integrable kernels. The third method is a discretization of the Dunford-Taylor formula. We discuss pros and cons of each method, error estimates, and document their performance with a few numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-05T20:10:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional diffusion",
      "numerical methods",
      "error estimates",
      "pde approach",
      "spectral definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}