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

  • Sylvie Boldo
  • François Clément
  • Jean-Christophe Filliâtre
  • Micaela Mayero
  • Guillaume Melquiond
  • Pierre Weis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)


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.


partial differential equation acoustic wave equation numerical scheme Coq formal proofs 


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sylvie Boldo
    • 1
    • 2
  • François Clément
    • 3
  • Jean-Christophe Filliâtre
    • 2
    • 1
  • Micaela Mayero
    • 4
    • 5
  • Guillaume Melquiond
    • 1
    • 2
  • Pierre Weis
    • 3
  1. 1.INRIA Saclay - Île-de-France, ProValOrsay
  2. 2.LRIUniversité Paris-Sud, CNRSOrsay
  3. 3.INRIA Paris - Rocquencourt, EstimeLe Chesnay
  4. 4.LIPNUniversité Paris 13, LCRVilletaneuse
  5. 5.LIPArénaire (INRIA Grenoble - Rhône-Alpes, CNRS UMR 5668, UCBL, ENS Lyon)Lyon

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