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-ordinary differential equation (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 as stable a way as index-2 Hessenberg DDAEs. We also comment on some practical aspects of the numerical solution of these problems.