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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 | Source: | Numerische mathematik, 2018, v. 138, no. 1, p. 101-131 | 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. | Publisher: | Springer | Journal: | Numerische mathematik | 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 |
Appears in Collections: | Journal/Magazine Article |
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