THE NUMERICAL-SOLUTION OF DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS OF RETARDED AND NEUTRAL TYPE

In this paper we consider the numerical solution of initial-value dela y-differential-algebraic equations (DDAEs) of retarded and neutral typ es, 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 di fferential equation (DODE). We present convergence results for linear multistep and Runge-Kutta methods applied to DDAEs of index 1 and 2 an d show how higher-index Hessenberg DDAEs can be formulated in as stabl e a way as index-2 Hessenberg DDAEs. We also comment on some practical aspects of the numerical solution of these problems.