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.