Open AccessMaximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations
Author(s) -
Carlos Lizama,
Marina MurilloArcila
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2022032
Subject(s) - quadrature (astronomy) , mathematics , convolution (computer science) , lebesgue integration , pure mathematics , discrete mathematics , computer science , machine learning , artificial neural network , electrical engineering , engineering
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 \begin{document}$ \theta $\end{document} -method as well as the backward differentiation formulas and the \begin{document}$ L1 $\end{document} -scheme. Fractional versions of these schemes, some of them completely new, are also shown, as well as their representation by means of the Grünwald–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.