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| HAL : inria-00450789, version 3 |
| arXiv : 1005.0824 |
| DOI : 10.1007/978-3-642-14052-5_12 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| ITP'10 - Interactive Theorem Proving, Edinburgh : United Kingdom (2010) |
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| Versions disponibles | v1 (27-01-2010) | v2 (05-05-2010) | v3 (14-11-2011) |
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| Formal Proof of a Wave Equation Resolution Scheme: the Method Error |
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Sylvie Boldo 1, 2François Clément 3 |
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| (11/07/2010) |
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| Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest one and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical pen-and-paper proofs. To our knowledge, this is the first time such kind of mathematical proof is machine-checked. |
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| 1 : | PROVAL (INRIA Saclay - Ile de France) |
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INRIA – Université Paris XI - Paris Sud – CNRS : UMR |
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| 2 : | Laboratoire de Recherche en Informatique (LRI) |
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CNRS : UMR8623 – Université Paris XI - Paris Sud |
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| 3 : | ESTIME (INRIA Paris-Rocquencourt) |
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INRIA |
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| 4 : | Laboratoire d'informatique de Paris-nord (LIPN) |
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CNRS : UMR7030 – Université Paris XIII - Paris Nord |
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| 5 : | ARENAIRE (Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme) |
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INRIA – CNRS : UMR5668 – Université Claude Bernard - Lyon I – École Normale Supérieure - Lyon |
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| Domaine | : | Informatique/Logique en informatique Mathématiques/Analyse numérique |
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| partial differential equation – acoustic wave equation – numerical scheme – Coq formal proofs |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| inria-00450789, version 3 | |
| http://hal.inria.fr/inria-00450789 | |
| oai:hal.inria.fr:inria-00450789 | |
| Contributeur : Francois Clement | |
| Soumis le : Mercredi 11 Mai 2011, 17:14:01 | |
| Dernière modification le : Mardi 29 Novembre 2011, 11:54:20 | |
