We formally prove the C program that implements a simple 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 the floating-point computation leads to round-off errors. We formally specify in Coq the numerical scheme, prove both the method error and the round-off error of the program, and derive an upper bound for the total error. This proves the adequacy of the C program to the numerical scheme and the convergence of the effective computation. To our knowledge, this is the first time a numerical analysis program is fully machine-checked.

Keywords: Formal proof of numerical program; Convergence of numerical scheme; Proof of C program; Coq formal proof; Acoustic wave equation; Partial differential equation; Rounding error analysis

Keywords: Why3

Keywords: Why3

Keywords: Why3