Numerical methods for fractional diffusion

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...

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Autores principales: Bonito, A., Borthagaray, J.P., Nochetto, R.H., Otárola, E., Salgado, A.J.
Formato: JOUR
Materias:
Computer science
Visualization
Discretizations
Error estimates
Fractional diffusion
Higher dimensions
Integral formulations
Numerical approximations
Numerical experiments
Taylor formula
Numerical methods
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14329360_v19_n5-6_p19_Bonito
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_14329360_v19_n5-6_p19_Bonito
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spelling todo:paper_14329360_v19_n5-6_p19_Bonito2023-10-03T16:14:09Z Numerical methods for fractional diffusion Bonito, A. Borthagaray, J.P. Nochetto, R.H. Otárola, E. Salgado, A.J. Computer science Visualization Discretizations Error estimates Fractional diffusion Higher dimensions Integral formulations Numerical approximations Numerical experiments Taylor formula Numerical methods 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. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14329360_v19_n5-6_p19_Bonito
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Computer science
Visualization
Discretizations
Error estimates
Fractional diffusion
Higher dimensions
Integral formulations
Numerical approximations
Numerical experiments
Taylor formula
Numerical methods
spellingShingle Computer science
Visualization
Discretizations
Error estimates
Fractional diffusion
Higher dimensions
Integral formulations
Numerical approximations
Numerical experiments
Taylor formula
Numerical methods
Bonito, A.
Borthagaray, J.P.
Nochetto, R.H.
Otárola, E.
Salgado, A.J.
Numerical methods for fractional diffusion
topic_facet Computer science
Visualization
Discretizations
Error estimates
Fractional diffusion
Higher dimensions
Integral formulations
Numerical approximations
Numerical experiments
Taylor formula
Numerical methods
description 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. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
format JOUR
author Bonito, A.
Borthagaray, J.P.
Nochetto, R.H.
Otárola, E.
Salgado, A.J.
author_facet Bonito, A.
Borthagaray, J.P.
Nochetto, R.H.
Otárola, E.
Salgado, A.J.
author_sort Bonito, A.
title Numerical methods for fractional diffusion
title_short Numerical methods for fractional diffusion
title_full Numerical methods for fractional diffusion
title_fullStr Numerical methods for fractional diffusion
title_full_unstemmed Numerical methods for fractional diffusion
title_sort numerical methods for fractional diffusion
url http://hdl.handle.net/20.500.12110/paper_14329360_v19_n5-6_p19_Bonito
work_keys_str_mv AT bonitoa numericalmethodsforfractionaldiffusion
AT borthagarayjp numericalmethodsforfractionaldiffusion
AT nochettorh numericalmethodsforfractionaldiffusion
AT otarolae numericalmethodsforfractionaldiffusion
AT salgadoaj numericalmethodsforfractionaldiffusion
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