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Discrete maximal regularity of time-stepping schemes for fractional evolution equations

In this work, we establish the maximal [Formula: see text] -regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text] , [Formula: see text] , in time. These schemes include convolution quadratures generated by b...

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Detalles Bibliográficos
Autores principales: Jin, Bangti, Li, Buyang, Zhou, Zhi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5762870/
https://www.ncbi.nlm.nih.gov/pubmed/29375159
http://dx.doi.org/10.1007/s00211-017-0904-8
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author Jin, Bangti
Li, Buyang
Zhou, Zhi
author_facet Jin, Bangti
Li, Buyang
Zhou, Zhi
author_sort Jin, Bangti
collection PubMed
description In this work, we establish the maximal [Formula: see text] -regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text] , [Formula: see text] , in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank–Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735–758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157–176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.
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spelling pubmed-57628702018-01-25 Discrete maximal regularity of time-stepping schemes for fractional evolution equations Jin, Bangti Li, Buyang Zhou, Zhi Numer Math (Heidelb) Article In this work, we establish the maximal [Formula: see text] -regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text] , [Formula: see text] , in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank–Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735–758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157–176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems. Springer Berlin Heidelberg 2017-07-22 2018 /pmc/articles/PMC5762870/ /pubmed/29375159 http://dx.doi.org/10.1007/s00211-017-0904-8 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Jin, Bangti
Li, Buyang
Zhou, Zhi
Discrete maximal regularity of time-stepping schemes for fractional evolution equations
title Discrete maximal regularity of time-stepping schemes for fractional evolution equations
title_full Discrete maximal regularity of time-stepping schemes for fractional evolution equations
title_fullStr Discrete maximal regularity of time-stepping schemes for fractional evolution equations
title_full_unstemmed Discrete maximal regularity of time-stepping schemes for fractional evolution equations
title_short Discrete maximal regularity of time-stepping schemes for fractional evolution equations
title_sort discrete maximal regularity of time-stepping schemes for fractional evolution equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5762870/
https://www.ncbi.nlm.nih.gov/pubmed/29375159
http://dx.doi.org/10.1007/s00211-017-0904-8
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