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NCTS Webinar on Nonlinear Evolutionary Dynamics
13:30 - 15:00, April 24, 2024 (Wednesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
An Introduction to Computer-Assisted Proofs for Dynamical Systems: How to Turn a Numerical Simulation into a Mathematical Theorem
Maxime Breden (École Polytechnique)

The goal of a posteriori validation methods is to get a quantitative and rigorous description of some specific solutions of nonlinear dynamical systems, based on numerical simulations, which helps shed some light on the global dynamics. 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.
In this talk I will present the main ideas behind these techniques, describe a rather general framework in which they can be applied, and showcase their interest by presenting examples of application related to population dynamics, fluid dynamics and shear-induced chaos.
Meeting number (access code): 2518 295 8662
Meeting password: acEtwymK235
Organizers: Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NCHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Alejandro López-Nieto (NTU), Chang-Hong Wu (NYCU)


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