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Uniformly accurate numerical schemes 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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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02619512
Contributor : Léopold Trémant <>
Submitted on : Monday, May 25, 2020 - 5:38:55 PM
Last modification on : Saturday, April 3, 2021 - 3:08:39 AM

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  • HAL Id : hal-02619512, version 1
  • ARXIV : 2005.12540

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Philippe Chartier, Mohammed Lemou, Léopold Trémant. Uniformly accurate numerical schemes for a class of dissipative systems. 2020. ⟨hal-02619512v1⟩

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