%0 Journal Article 
%A Lizama, Carlos
%A Murillo Arcila, Marina
%T Maximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations
%D 2022
%@ 1553-5231

%U http://hdl.handle.net/10498/35344
%X 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.
%K Maximal regularity
%K time-stepping schemes
%K convolution quadrature
%K nonlocal time-stepping schemes
%~ Universidad de Cádiz