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

Jin, B; Li, B; Zhou, Z; (2017) Discrete maximal regularity of time-stepping schemes for fractional evolution equations. Numerische Mathematik 10.1007/s00211-017-0904-8. (In press). Green open access

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Abstract

In this work, we establish the maximal (Formula presented.)-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order (Formula presented.), (Formula presented.), 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.

Type: Article
Title: Discrete maximal regularity of time-stepping schemes for fractional evolution equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-017-0904-8
Publisher version: http://doi.org/10.1007/s00211-017-0904-8
Language: English
Additional information: Copyright © 2017 The Author(s). This 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.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1561159
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