RT journal article
T1 Maximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Maximal regularity
K1 time-stepping schemes
K1 convolution quadrature
K1 nonlocal time-stepping schemes
AB We study discrete time maximal regularity in Lebesgue spaces ofsequences for time-stepping schemes arising from Lubich’s convolution quadraturemethod. We show minimal properties on the quadrature weights thatdetermines a wide class of implicit schemes. For an appropriate choice of theweights, we are able to identify the θ-method as well as the backward differentiationformulas and the L1-scheme. Fractional versions of these schemes,some of them completely new, are also shown, as well as their representationby means of the Gr¨unwald–Letnikov fractional order derivative. Our resultsextend and improve some recent results on the subject and provide new insightson the basic nature of the weights that ensure maximal regularity.
PB AIMS
SN 1553-5231
YR 2022
FD 2022
LK http://hdl.handle.net/10498/35344
UL http://hdl.handle.net/10498/35344
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026