Formal Proof of a Wave Equation Resolution Scheme: the Method Error
Logic in Computer Science
2011-11-15 v2 Numerical Analysis
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.
Cite
@article{arxiv.1005.0824,
title = {Formal Proof of a Wave Equation Resolution Scheme: the Method Error},
author = {Sylvie Boldo and François Clément and Jean-Christophe Filliâtre and Micaela Mayero and Guillaume Melquiond and Pierre Weis},
journal= {arXiv preprint arXiv:1005.0824},
year = {2011}
}
Comments
replaces arXiv:1001.4898