The goal of a posteriori validation methods is to get a quantitative and
rigorous description of some specific solutions of nonlinear ODEs or PDEs,
based on numerical simulations. The general strategy consists in combining
a priori and a posteriori error estimates, interval arithmetic, and a fixed
point theorem applied to a quasi-Newton operator. Starting from a numerically computed approximate solution, one can then prove the existence
of a true solution in a small and explicit neighborhood of the numerical
approximation.
In this talk I will present the main ideas behind these techniques, describe
a rather general framework in which they can be applied, and showcase their
interest by presenting examples of application in population dynamics, fluid
dynamics and corrosion problems.