Numerical Methods for Fractional Diffusion
For researchers working on numerical methods for non-local diffusion processes, this paper offers a comparative analysis of three approaches, but the contribution is incremental.
The paper presents and compares three numerical schemes for fractional diffusion, providing error estimates and performance benchmarks through numerical experiments.
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.