Applied & Computational Mathematics seminar: Validated integration for state-dependent delay equations

Speaker:  Kevin Church, McGill University

Title:  Validated integration for state-dependent delay equations

Abstract:   

Differential equations with state-dependent delay arise naturally in problems from electrodynamics, communication networks, and biological processes, to name a few areas. However, if one surveys the literature on delay differential equations, one finds that state-dependent delay equations (SDDE) are the exception rather than the rule. One reason for this is that state-dependent delays present a massive theoretical difficulty compared to constant delays. For example, there remain long-standing open problems concerning the regularity of the semiflows and invariant manifolds of SDDE that are comparatively trivial when restricted to constant delays. From the perspective of verified numerical integration of SDDE, there are difficulties associated to the handling of “compositional nonlinearities”. The latter are the defining feature of this class of equations.

In this seminar, I will present a validated integration scheme for SDDE based on polynomial interpolation. To set the stage, I will survey some recent theoretical and computational advances in the area of SDDE, while pointing out a few open problems. I will then present the integration scheme and give some background on the computer-assisted proof framework used for the validation.

Time:   Friday, November 19, 2021, 1:30pm – 2:30pm

Place:  Zoom - https://gmu.zoom.us/j/96953045320