Numerical Methods for Fractional Diffusion

Andrea Bonito, Juan Pablo Borthagaray, Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado

Published 2017-07-05Version 1

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.