CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

30 mars 2021 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Computer-assisted proofs for Cauchy problems of delay equations and PDEs via Chebyshev series

Séminaire par Jean-Philippe Lessard (Université McGill, Canada)

In this talk we introduce recent general methods to rigorously compute solutions of infinite dimensional Cauchy problems. The idea is to expand the solutions in time using Chebyshev series and use the contraction mapping theorem to construct a neighbourhood about an approximate solution which contains the exact solution of the Cauchy problem. We apply the methods to delay differential equations and to semi-linear parabolic partial differential equations.