Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/74469
Title: Discrete maximal regularity of time-stepping schemes for fractional evolution equations
Authors: Jin, B
Li, B 
Zhou, Z 
Issue Date: 2018
Publisher: Springer
Source: Numerische mathematik, 2018, v. 138, no. 1, p. 101-131 How to cite?
Journal: Numerische mathematik 
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.
URI: http://hdl.handle.net/10397/74469
ISSN: 0029-599X
EISSN: 0945-3245
DOI: 10.1007/s00211-017-0904-8
Rights: ©The Author(s) 2017. This article is an open access publication
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