Numerical Methods for Fractional Diffusion
Numerical Analysis
2019-02-05 v1
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.
Cite
@article{arxiv.1707.01566,
title = {Numerical Methods for Fractional Diffusion},
author = {Andrea Bonito and Juan Pablo Borthagaray and Ricardo H. Nochetto and Enrique Otarola and Abner J. Salgado},
journal= {arXiv preprint arXiv:1707.01566},
year = {2019}
}