Proper Orthogonal Decomposition and Dynamic Mode Decomposition of Delay-Differential Equations

Abstract

Our work is based on the observation that delay-differential equations can be recast as partial differential equations of two variables. Thus the numerical solution of the delay equation can be thought of as a spatio-temporal process, and snapshot based methods like Proper Orthogonal Decomposition and Dynamic Mode Decomposition allow us to compute the eigenvalues of the evolution operator. The rightmost eigenvalues of the Hayes equation can be well approximated.