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arXiv · 1112.1795

Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program

Sylvie Boldo·Francois Clement·Jean-Christophe Filliâtre·Micaela Mayero·Guillaume Melquiond·Pierre Weis
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Abstract

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.

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Sylvie Boldo, Francois Clement, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, Pierre Weis. 2011-12-08. Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program. https://doi.org/10.1007/s10817-012-9255-4

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