Unbiased `walk-on-spheres' Monte Carlo methods for the fractional Laplacian

Kyprianou, Andreas E.; Osojnik, Ana; Shardlow, Tony

doi:10.48550/arxiv.1609.03127

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2018

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“…For several dimensions the literature is rather scarce. A Monte Carlo algorithm that avoids dealing with the singular kernel was proposed in [77].…”

Section: Femmentioning

confidence: 99%

Numerical methods for fractional diffusion

Bonito

Borthagaray

Nochetto

et al. 2018

Comput. Visual Sci.

158

109

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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.Date: Draft version of July 7, 2017.

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“…For several dimensions the literature is rather scarce. A Monte Carlo algorithm that avoids dealing with the singular kernel was proposed in [77].…”

Section: Femmentioning

confidence: 99%