| Issue |
ESAIM: Proc.
Volume 30, August 2010
CEMRACS 2009: Mathematical Modelling in Medicine
|
|
|---|---|---|
| Page(s) | 53 - 69 | |
| DOI | https://doi.org/10.1051/proc/2010006 | |
| Published online | 07 December 2010 | |
High-order WENO scheme for polymerization-type equations*
1
Université Pierre et Marie Curie-Paris 6, UMR 7598 LJLL,
BC187, 4, place de
Jussieu, F-75252
Paris cedex 5,
France
email:
gabriel@ann.jussieu.fr
2
Equipe-Projet SIMPAF, Centre de Recherche INRIA Lille Nord
Europe, Parc Scientifique de la Haute Borne, 40, avenue Halley
B.P. 70478, F-59658
Villeneuve dAscq cedex,
France
3
Laboratoire Paul
Painlevé, UMR 8524, CNRS-Université des Sciences et Technologies de Lille Cité
Scientifique, F-59655
Villeneuve dAscq Cedex,
France
email: Leon-matar.Tine@math.univ-lille1.fr
4
Laboratoire LANI - UFR SAT, Université Gaston Berger de
Saint-Louis, B. P.
234
Saint-Louis,
Sénégal
Polymerization of proteins is a biochemical process involved in different diseases. Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In this paper we consider a general polymerization model and propose a high-order numerical scheme to investigate the behavior of the solution. An important property of the equation is the mass conservation. The WENO scheme is built to preserve the total mass of proteins along time.
Résumé
Le processus biophysique de polymérisation de protéines entre en jeu dans différentes maladies. Mathématiquement, ceci est généralement modélisé par des équations de type agrégation-fragmentation. Dans cet article nous considérons un modèle général de polymérisation et proposons un schéma d’ordre élevé pour sa résolution numérique. Une propriété importante de l’équation est la conservation de la masse. Le schéma WENO est construit pour conserver la masse totale de protéines au cours du temps.
This work has been done with the financial supports of
- the ANR contract TOPPAZ, allocation grant n4243, http://www-roc.inria.fr/bang/TOPPAZ/
- the CEA-Institute of Emerging Diseases and Innovative Therapies, Route du Panorama, Bat.60, F-92265 Fontenay-aux-Roses.
© EDP Sciences, ESAIM 2010
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