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

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

2010-05-05

arxiv.org/abs/1005.0824v2

Interactive Theorem Proving 6172 (2010) 147-162

Computer Science

Logic in Computer Science

replaces arXiv:1001.4898

Scientific paper

10.1007/978-3-642-14052-5_12

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.

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