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.
CITATION STYLE
Bonito, A., Borthagaray, J. P., Nochetto, R. H., Otárola, E., & Salgado, A. J. (2018). Numerical methods for fractional diffusion. Computing and Visualization in Science, 19(5–6), 19–46. https://doi.org/10.1007/s00791-018-0289-y
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