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| HAL : hal-00175003, version 1 |
| DOI : 10.1080/00207160701458716 |
| Fiche détaillée |  Récupérer au format |
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| International Journal of Computer Mathematics 84, 6 (2007) 749 - 765 |
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| On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients |
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Stéphane Descombes 1Marc Massot 2 |
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| (01/06/2007) |
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| In this paper we study the approximation by splitting techniques of the ordinary differential equation Udot+A U+B U=0, U(0)=U0 with A and B two matrices. We assume that we have a stiff problem in the sense that A is ill-conditionned and U0 is a vector which is the discretization of a function with a very high derivative. This situation may appear for example when we study the discretization of a partial differential equation. We prove some error estimates for two general matrices and in the stiff case, where the estimates are independent of U0 and the commutator between A and B. This paper is dedicated to Michel Crouzeix. |
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| 1 : | Unité de Mathématiques Pures et Appliquées (UMPA-ENSL) |
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CNRS : UMR5669 – École Normale Supérieure - Lyon |
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| 2 : | Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C) |
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CNRS : UPR288 – Ecole Centrale Paris |
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| 3 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Analyse numérique |
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| Splitting approximation errors – Reaction-diffusion equations – High spatial gradients |
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| hal-00175003, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00175003 | |
| oai:hal.archives-ouvertes.fr:hal-00175003 | |
| Contributeur : Marc Massot | |
| Soumis le : Mercredi 26 Septembre 2007, 10:37:30 | |
| Dernière modification le : Jeudi 15 Novembre 2007, 15:16:57 | |
