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...
| Autores: | , |
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| 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 |
| 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. |
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