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Wave equation numerical resolution: a comprehensive mechanized proof of a C program. (English) Zbl 1267.68208

Summary: 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.

MSC:

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
35L05 Wave equation
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65G50 Roundoff error
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