Dynamics of Delay Equations, Theory and Applications - Abstract

Unger, Benjamin

Numerical solution of implicit delay differential equations

In this talk we present a numerical framework to solve implicit delay differential equations of the form F(t,x(t),dotx(t),x(t-tau)) = 0. Such systems present several challenges, requiring index-reduction, consistent initialization, non-smooth crossings at integer multiples of the delay time tau, and a-causal behavior. We demonstrate these challenges via several examples and offer strategies to regularize the system prior to numerical integration. We will also discuss the solution of multibody systems subject to delayed feedback.