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Computing and Visualization in Science

, Volume 19, Issue 5–6, pp 19–46 | Cite as

Numerical methods for fractional diffusion

  • Andrea Bonito
  • Juan Pablo Borthagaray
  • Ricardo H. NochettoEmail author
  • Enrique Otárola
  • Abner J. Salgado
Special Issue FEM Symposium 2017

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.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Andrea Bonito
    • 1
  • Juan Pablo Borthagaray
    • 2
  • Ricardo H. Nochetto
    • 3
    Email author
  • Enrique Otárola
    • 4
  • Abner J. Salgado
    • 5
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.IMAS - CONICET and Departamento de MatemáticaFCEyN - Universidad de Buenos AiresBuenos AiresArgentina
  3. 3.Department of Mathematics and Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA
  4. 4.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaisoChile
  5. 5.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

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