The Numerical Solution of Delay-Differential-Algebraic Equations of Retarded and Neutral Type

In this paper we consider the numerical solution of initial value delay-differential-algebraic equations (DDAEs) of retarded and neutral types, with a structure corresponding to that of Hessenberg DAEs. We give conditions under which the DDAE is well-conditioned, and show how the DDAE is related to an underlying retarded or neutral delay-ODE (DODE). We present convergence results for linear multistep and Runge-Kutta methods applied to DDAEs of index 1 and 2, and show how higher-index Hessenberg DDAEs can be formulated in a stable way as index-2 Hessenberg DDAEs.