Formal Proof of a Wave Equation Resolution Scheme: the Method Error

Authors:
  • SBSylvie Boldo
    Sylvie Boldo
  • FCFrançois Clément
    François Clément
  • JFJean-Christophe Filliâtre
    Jean-Christophe Filliâtre
  • MMMicaela Mayero
    Micaela Mayero
  • GMGuillaume Melquiond
    Guillaume Melquiond
  • PWPierre Weis
    Pierre Weis
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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.