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    Por favor, use este identificador para citar o enlazar este ítem:https://uvadoc.uva.es/handle/10324/62691

    Título
    Avoiding order reduction phenomenon for general linear methods when integrating linear problems with time dependent boundary values
    Autor
    Reguera, N.
    Alonso Mallo, IsaíasAutoridad UVA Orcid
    Año del Documento
    2024
    Editorial
    Elsevier
    Descripción
    Producción Científica
    Documento Fuente
    Journal of Computational and Applied Mathematics, 2024, vol. 439, 115629
    Resumen
    When applied to stiff problems, the effective order of convergence of general linear methods is governed by their stage order, which is less than or equal to the classical order of the method. This produces an order reduction phenomenon, present in all general linear methods except those with high stage order, in a manner similar to that observed in other time integrators with internal stages. In this paper, we investigate the order reduction which arises when general linear methods are used as time integrators when using the method of lines for solving numerically initial boundary value problems with time dependent boundary values. We propose a technique, based on making an appropriate choice of the boundary values for the internal stages, with which it is possible to recover one unit of order, as we prove in this work. As expected, this implies a considerable improvement for the general linear methods suffering order reduction. Moreover, numerical experiments show that the improvement is not only in these cases, but that, even when the order reduction is not expected, the size of the errors is drastically reduced by using the technique proposed in this paper.
    Materias (normalizadas)
    Matemáticas
    Algebra lineal
    Materias Unesco
    12 Matemáticas
    Palabras Clave
    Order reduction
    General linear methods
    Initial boundary value problems
    Reducción de pedido
    Métodos lineales generales
    Problemas de valores límite iniciales
    ISSN
    0377-0427
    Revisión por pares
    SI
    DOI
    10.1016/j.cam.2023.115629
    Patrocinador
    Ministerio de Ciencia e Innovación y Ministerio de Universidades (project PGC2018-101443-B-100)
    Junta de Castilla y León (Grant numbers VA169P20 and VA193P20)
    Version del Editor
    https://www.sciencedirect.com/science/article/pii/S0377042723005733?via%3Dihub
    Propietario de los Derechos
    © 2023 The Authors
    Idioma
    eng
    URI
    https://uvadoc.uva.es/handle/10324/62691
    Tipo de versión
    info:eu-repo/semantics/publishedVersion
    Derechos
    openAccess
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    • DEP51 - Artículos de revista [145]
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