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. Key words: partial differential equation, acoustic wave equation, numerical scheme, Coq formal proofs

• Type: Conference
• Year: 2010
• Where: ITP
• Authors: Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, Pierre Weis
• Keywords: Acoustic Wave Equation, ITP 2010, Mathematics, Numerical Scheme, One-dimensional Acoustic Wave