  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.
