@misc{10498/35344,
year = {2022},
url = {http://hdl.handle.net/10498/35344},
abstract = {We study discrete time maximal regularity in Lebesgue spaces of
sequences for time-stepping schemes arising from Lubich’s convolution quadrature
method. We show minimal properties on the quadrature weights that
determines a wide class of implicit schemes. For an appropriate choice of the
weights, we are able to identify the θ-method as well as the backward differentiation
formulas and the L1-scheme. Fractional versions of these schemes,
some of them completely new, are also shown, as well as their representation
by means of the Gr¨unwald–Letnikov fractional order derivative. Our results
extend and improve some recent results on the subject and provide new insights
on the basic nature of the weights that ensure maximal regularity.},
publisher = {AIMS},
keywords = {Maximal regularity},
keywords = {time-stepping schemes},
keywords = {convolution quadrature},
keywords = {nonlocal time-stepping schemes},
title = {Maximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations},
doi = {10.3934/DCDS.2022032},
author = {Lizama, Carlos and Murillo Arcila, Marina},
}