A uniformly accurate numerical method for a class of dissipative systems
Abstract
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale method by decomposing this problem into a micro-macro system where the original stiffness is broken. We show that this new problem can therefore be simulated with a uniform order of accuracy using standard explicit numerical schemes. In other words, it is possible to solve the micro-macro problem with a cost independent of the stiffness (a.k.a. uniform cost), such that the error is also uniform. This method is successfully applied to two hyperbolic systems with and without non-linearities, and is shown to circumvent the phenomenon of order reduction.
Fichier principal
0_mima_dissip.pdf (461.92 Ko)
Télécharger le fichier
0_mima_dissip.run.xml (2.31 Ko)
Télécharger le fichier
cv_hyperb-eps-converted-to.pdf (28.37 Ko)
Télécharger le fichier
cv_hyperb_erk2-eps-converted-to.pdf (29.67 Ko)
Télécharger le fichier
cv_oscill_max_err_and_dev2-eps-converted-to.pdf (30.18 Ko)
Télécharger le fichier
cv_telegraph-eps-converted-to.pdf (28.82 Ko)
Télécharger le fichier
cv_telegraph_erk2-eps-converted-to.pdf (30.37 Ko)
Télécharger le fichier
ord_gain_cons_law-eps-converted-to.pdf (18.04 Ko)
Télécharger le fichier
ord_gain_oscill-eps-converted-to.pdf (20.46 Ko)
Télécharger le fichier
ord_gain_telegraph-eps-converted-to.pdf (18.04 Ko)
Télécharger le fichier
Origin : Files produced by the author(s)