Formal Proof of a Wave Equation Resolution Scheme: the Method Error

Sylvie Boldo 1, 2 François Clément 3, * Jean-Christophe Filliâtre 1, 2 Micaela Mayero 4, 5 Guillaume Melquiond 1, 2 Pierre Weis 3
* Corresponding author
1 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
5 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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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Conference papers
Matt Kaufmann and Lawrence C. Paulson. ITP'10 - Interactive Theorem Proving, Jul 2010, Edinburgh, United Kingdom. Springer, 6172, pp.147-162, 2010, Lecture Notes in Computer Science; Interactive Theorem Proving. <10.1007/978-3-642-14052-5_12>
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Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Formal Proof of a Wave Equation Resolution Scheme: the Method Error. Matt Kaufmann and Lawrence C. Paulson. ITP'10 - Interactive Theorem Proving, Jul 2010, Edinburgh, United Kingdom. Springer, 6172, pp.147-162, 2010, Lecture Notes in Computer Science; Interactive Theorem Proving. <10.1007/978-3-642-14052-5_12>. <inria-00450789v3>

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