How to improve the decay of the numerical error for large times: the case of dissipative BGK systems

Maya Briani (1) , Denise Aregba-Driollet (2) , Roberto Natalini (1)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 IMB - Institut de Mathématiques de Bordeaux

We introduce new finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using accurate analytical time-decay properties of the local truncation error, it is possible to design schemes based on standard upwinding schemes, which are increasingly accurate for large times when computing small perturbations of constants asymptotic states.

Domaines: Analyse numérique [math.NA]

Maya Briani, Denise Aregba-Driollet, Roberto Natalini. How to improve the decay of the numerical error for large times: the case of dissipative BGK systems. HYP2012 Padova, 2012, Italy. pp.365-372. ⟨hal-00959562⟩