Asymptotic high order mass-preserving schemes for a hyperbolic model of chemotaxis (Articolo in rivista)

Type
Label
  • Asymptotic high order mass-preserving schemes for a hyperbolic model of chemotaxis (Articolo in rivista) (literal)
Anno
  • 2012-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1137/100803067 (literal)
Alternative label
  • Natalini, R.; Ribot, M. (2012)
    Asymptotic high order mass-preserving schemes for a hyperbolic model of chemotaxis
    in SIAM journal on numerical analysis (Print); SIAM Publications, Philadelphia (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Natalini, R.; Ribot, M. (literal)
Pagina inizio
  • 883 (literal)
Pagina fine
  • 905 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://epubs.siam.org/doi/abs/10.1137/100803067 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 50 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 22 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 2 (literal)
Note
  • Mathematical Reviews on the web (MathSciNet) (literal)
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • 1. CNR, Ist Applicaz Calcolo Mauro Picone, I-00185 Rome, Italy 2. Univ Nice Sophia Antipolis, CNRS, UMR 6621, Lab JA Dieudonne, F-06108 Nice 02, France (literal)
Titolo
  • Asymptotic high order mass-preserving schemes for a hyperbolic model of chemotaxis (literal)
Abstract
  • We introduce a new class of finite difference schemes for approximating the solutions to an initial-boundary value problem on a bounded interval for a one-dimensional dissipative hyperbolic system with an external source term, which arises as a simple model of chemotaxis. Since the solutions to this problem may converge to nonconstant asymptotic states for large times, standard schemes usually fail to yield a good approximation. Therefore, we propose a new class of schemes, which use an asymptotic higher order correction, second and third order in our examples, to balance the effects of the source term and the influence of the asymptotic solutions. Special care is needed to deal with boundary conditions to avoid harmful loss of mass. Convergence results are proved for these new schemes, and several numerical tests are presented and discussed to verify the effectiveness of their behavior. (literal)
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