TY - GEN
T1 - Formal proof of a wave equation resolution scheme
T2 - 1st International Conference on Interactive Theorem Proving, ITP 2010
AU - Boldo, Sylvie
AU - Clément, François
AU - Filliâtre, Jean Christophe
AU - Mayero, Micaela
AU - Melquiond, Guillaume
AU - Weis, Pierre
PY - 2010/1/1
Y1 - 2010/1/1
N2 - 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.
AB - 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.
KW - Coq formal proofs
KW - acoustic wave equation
KW - numerical scheme
KW - partial differential equation
UR - https://www.scopus.com/pages/publications/77955254707
U2 - 10.1007/978-3-642-14052-5_12
DO - 10.1007/978-3-642-14052-5_12
M3 - Conference contribution
AN - SCOPUS:77955254707
SN - 3642140513
SN - 9783642140518
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 147
EP - 162
BT - Interactive Theorem Proving - First International Conference, ITP 2010, Proceedings
PB - Springer Verlag
Y2 - 11 July 2010 through 14 July 2010
ER -