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Fecha
2025-02-05
Derechos de acceso
info:eu-repo/semantics/openAccess
Título de la revista
ISSN de la revista
Título del volumen
Editorial
Springer
Citas
Resumen
Fractional dissipation is a powerful tool to study nonlocal physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational formulation of the model. In Jiménez and Ober-Blöbaum (J Nonlinear Sci 31:46, 2021), a new approach is proposed to deal with dissipative systems including fractionally damped systems in a variational way for both, the continuous and discrete setting. It is based on the doubling of variables and their fractional derivatives. The aim of this work is to derive higher-order fractional variational integrators by means of convolution quadrature (CQ) based on backward difference formulas. We then provide numerical methods that are of order 2 improving a previous result in Jiménez and Ober-Blöbaum (J Nonlinear Sci 31:46, 2021). The convergence properties of the fractional variational integrators and saturation effects due to the approximation of the fractional derivatives by CQ are studied numerically.
Descripción
The registered version of this article, first published in Journal of Nonlinear Science, is available online at the publisher's website: Springer, https://doi.org/10.1007/s00332-025-10131-0
La versión registrada de este artículo, publicado por primera vez en Journal of Nonlinear Science, está disponible en línea en el sitio web del editor: Springer, https://doi.org/10.1007/s00332-025-10131-0
La versión registrada de este artículo, publicado por primera vez en Journal of Nonlinear Science, está disponible en línea en el sitio web del editor: Springer, https://doi.org/10.1007/s00332-025-10131-0
Categorías UNESCO
Palabras clave
Convolution quadrature, Fractional derivatives, Fractional dissipative systems, Fractional differential equations, Variational principles, Variational integrators
Citación
Hariz Belgacem, K., Jiménez, F. & Ober-Blöbaum, S. Fractional Variational Integrators Based on Convolution Quadrature. J Nonlinear Sci 35, 38 (2025). https://doi.org/10.1007/s00332-025-10131-0
Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I