CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

March 30, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

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

Seminar presented by Jean-Philippe Lessard (McGill University, 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.