Date/Time Date(s) - 08/11/20243:30 pm - 4:30 pm
Location: Hamilton Hall, Room 305
Speaker: Dr. Maxime Brenden (Ecole polytechnique)
Title: An introduction to computer-assisted proofs for nonlinear equations: how to turn numerical simulation into theorem
Abstract: 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.
I will first present the main ideas behind these techniques on a simple example, then describe a rather general framework in which they can be applied, and finally, time permitting, discuss some recent applications.
Coffee will be served in the same room – HH 305 at 3pm – all are welcome.