Formal Proof of a Wave Equation Resolution Scheme: The Method Error
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- Boldo S., Clément F., Filliâtre JC., Mayero M., Melquiond G., Weis P. (2010) Formal Proof of a Wave Equation Resolution Scheme: The Method Error. In: Kaufmann M., Paulson L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg
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.
Keywordspartial differential equation acoustic wave equation numerical scheme Coq formal proofs
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