Maxime Breden: Thursday 9th Nov at 11:00am
The goal of a posteriori validation methods is to get a quantitative and rigorous description of some specific solutions of nonlinear dynamical sys- tems, often ODEs or PDEs, based on numerical simulations. The general strategy consists in combining a priori and a posteriori error estimates, in- terval arithmetic, and a fixed point theorem applied to a quasi-Newton op- erator. Starting from a numerically computed approximate solution, one can then prove the existence of a true solution in a small and explicit neigh- borhood of the numerical approximation.
I will first present the main ideas behind these techniques on a simple example, and then describe the results of a recent joint work with Jan Bouwe van den Berg and Ray Sheombarsing, in which we use these techniques to rigorously enclose solutions of some parabolic PDEs.