Numerical methods for fractional diffusion Academic Article uri icon

abstract

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

altmetric score

  • 1

author list (cited authors)

  • Bonito, A., Borthagaray, J. P., Nochetto, R. H., Otárola, E., & Salgado, A. J.

citation count

  • 52

publication date

  • March 2018