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Computer programs may go wrong due to exceptional behaviors, out-of-boundarray accesses, or simply coding errors. Thus, they cannot be blindly trusted.Scientific computing programs make no exception in that respect, and even bringspecific accuracy issues due to their massive use of floating-pointcomputations. Yet, it is uncommon to guarantee their correctness. Indeed, wehad to extend existing methods and tools for proving the correct behavior ofprograms to verify an existing numerical analysis program. This C programimplements the second-order centered finite difference explicit scheme forsolving the 1D wave equation. In fact, we have gone much further as we havemechanically verified the convergence of the numerical scheme in order to get acomplete formal proof covering all aspects from partial differential equationsto actual numerical results. To the best of our knowledge, this is the firsttime such a comprehensive proof is achieved.

Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program