Skip to Main content Skip to Navigation

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.
Complete list of metadatas
Contributor : Francois Clement <>
Submitted on : Wednesday, January 27, 2010 - 11:20:20 AM
Last modification on : Tuesday, February 11, 2020 - 2:07:20 PM
Document(s) archivé(s) le : Friday, June 18, 2010 - 1:29:41 AM


Files produced by the author(s)


  • HAL Id : inria-00450789, version 1
  • ARXIV : 1005.0824



Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Formal Proof of a Wave Equation Resolution Scheme: the Method Error. [Research Report] RR-7181, 2010, pp.17. ⟨inria-00450789v1⟩



Record views


Files downloads