Date/Time
Date(s) - 08/11/2024
3:30 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.