High-order WENO scheme for Polymerization-type equations

Pierre Gabriel (1) , Léon Matar Tine (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 SIMPAF - SImulations and Modeling for PArticles and Fluids

Polymerization of proteins is a biochimical 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 fifth-order WENO scheme is built to preserve the total mass of proteins along time.

Mots clés: Aggregation-fragmentation equations; mass conservation; WENO numerical scheme; long-time asymptotic; polymerization process; size repartition

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Pierre Gabriel, Léon Matar Tine. High-order WENO scheme for Polymerization-type equations. ESAIM: Proceedings and Surveys, 2010, CEMRACS 2009: Mathematical Modelling in Medicine, 30, pp.53-69. ⟨10.1051/proc/2010006⟩. ⟨hal-00455472v2⟩