Wave Equation Numerical Resolution: Mathematics and Program

Details Wave Equation Numerical Resolution: Mathematics and Program Wave Equation Numerical Resolution: Mathematics and Program

2011-12-08

arxiv.org/abs/1112.1795v1

Computer Science

Logic in Computer Science

(2011)

Scientific paper

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.

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