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Convergence of a finite volume scheme for coagulation-fragmentation equations
Authors:Jean-Pierre Bourgade  Francis Filbet
Institution:Institut de Mathématiques de Toulouse, Université Toulouse III, 118, route de Narbonne 31062 Toulouse cedex 09, France ; Université Lyon, Université Lyon 1, CNRS, UMR 5208 - Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France
Abstract:This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation. A time explicit finite volume scheme is developed, based on a conservative formulation of the equation. It is shown to converge under a stability condition on the time step, while a first order rate of convergence is established and an explicit error estimate is given. Finally, several numerical simulations are performed to investigate the gelation phenomenon and the long time behavior of the solution.

Keywords:Coagulation-fragmentation equation  finite volume method
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