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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
Discrete maximal regularity of time-stepping schemes for fractional evolution equations
Bangti Jin1, Buyang Li2, Zhi Zhou2
11Department of Computer Science, University College London, Gower Street, London, WC1E 6BT UK.
Abstract:
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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