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Journal articles

A uniformly accurate numerical method for a class of dissipative systems

Philippe Chartier 1 Mohammed Lemou 2, 1 Léopold Trémant 1, *
* Corresponding author
1 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
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.
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Submitted on : Thursday, April 1, 2021 - 3:49:40 PM
Last modification on : Friday, May 20, 2022 - 9:04:53 AM



Philippe Chartier, Mohammed Lemou, Léopold Trémant. A uniformly accurate numerical method for a class of dissipative systems. Mathematics of Computation, American Mathematical Society, 2022, 91 (334), pp.843-869. ⟨10.1090/mcom/3688⟩. ⟨hal-02619512v2⟩



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