@inproceedings{1c616b41c0324371b0ce707dc2fff6e0,
title = "Formal proof of a wave equation resolution scheme: The method error",
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 scheme 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 this kind of mathematical proof is machine-checked.",
keywords = "Coq formal proofs, acoustic wave equation, numerical scheme, partial differential equation",
author = "Sylvie Boldo and Fran{\c c}ois Cl{\'e}ment and Filli{\^a}tre, \{Jean Christophe\} and Micaela Mayero and Guillaume Melquiond and Pierre Weis",
year = "2010",
month = jan,
day = "1",
doi = "10.1007/978-3-642-14052-5\_12",
language = "English",
isbn = "3642140513",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "147--162",
booktitle = "Interactive Theorem Proving - First International Conference, ITP 2010, Proceedings",
note = "1st International Conference on Interactive Theorem Proving, ITP 2010 ; Conference date: 11-07-2010 Through 14-07-2010",
}