Splitting and composition methods for explicit time-dependence in separable dynamical systems (Articolo in rivista)

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Label
  • Splitting and composition methods for explicit time-dependence in separable dynamical systems (Articolo in rivista) (literal)
Anno
  • 2010-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1016/j.cam.2010.06.018 (literal)
Alternative label
  • Blanes Sergio; Diele Fasma; Marangi Carmela; Ragni Stefania (2010)
    Splitting and composition methods for explicit time-dependence in separable dynamical systems
    in Journal of computational and applied mathematics
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Blanes Sergio; Diele Fasma; Marangi Carmela; Ragni Stefania (literal)
Pagina inizio
  • 646 (literal)
Pagina fine
  • 659 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.sciencedirect.com/science/article/pii/S0377042710003705 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 235 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 3 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Sergio Blanes, Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia, E-46022 Valencia, Spain; Fasma Diele, Istituto per le Applicazioni del Calcolo M. Picone,CNR, Via Amendola 122, 70126 Bari, Italy; Carmela Marangi, Istituto per le Applicazioni del Calcolo M. Picone,CNR, Via Amendola 122, 70126 Bari, Italy; Stefania Ragni, Facolt√† di Economia, Universit√† di Bari, Via Camillo Rosalba 56, 70100 Bari, Italy (literal)
Titolo
  • Splitting and composition methods for explicit time-dependence in separable dynamical systems (literal)
Abstract
  • We consider splitting methods for the numerical integration of separable non-autonomous differential equations. In recent years, splitting methods have been extensively used as geometric numerical integrators showing excellent performances (both qualitatively and quantitatively) when applied on many problems. They are designed for autonomous separable systems, and a substantial number of methods tailored for different structures of the equations have recently appeared. Splitting methods have also been used for separable non-autonomous problems either by solving each non-autonomous part separately or after each vector field is frozen properly. We show that both procedures correspond to introducing the time as two new coordinates. We generalize these results by considering the time as one or more further coordinates which can be integrated following either of the previous two techniques. We show that the performance as well as the order of the final method can strongly depend on the particular choice. We present a simple analysis which, in many relevant cases, allows one to choose the most appropriate split to retain the high performance the methods show on the autonomous problems. This technique is applied to different problems and its performance is illustrated for several numerical examples. (literal)
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