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arXiv · 1707.01566

Numerical Methods for Fractional Diffusion

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

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Andrea Bonito, Juan Pablo Borthagaray, Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado. 2017-07-05. Numerical Methods for Fractional Diffusion. https://doi.org/10.1007/s00791-018-0289-y

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