Third Year Candidacy Requirement: Modified Vector Fields and Functional Equivariance

Abstract: Some numerial integrators preserve geometric properties of the flow of differential equations. Linear and quadratic first integrals and their preservation by numerical integrators has been studied extensively. McLachlan and Stern introduced the idea of F-functional equivariance that provides a new framework to talk about the preservation of first integrals as well as other notable observables of a dynamical system. In this talk, I will give an overview of these ideas as well as an introduction to the theory of backward error analysis. I will then pose some preliminary results and questions addressing how F-functional equivariance may be talked about through a backward error analysis perspective.

Host: Ari Stern