Maximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations

[EN] 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 t...

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Detalles Bibliográficos
Autores: Lizama, Carlos, Murillo Arcila, Marina
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/202051
Acceso en línea:https://riunet.upv.es/handle/10251/202051
Access Level:acceso abierto
Palabra clave:Maximal regularity
Time-stepping schemes
Convolution quadrature
Nonlocal time-stepping schemes
Descripción
Sumario:[EN] 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 theta-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 Grunwald-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.