A survey on numerical methods for the simulation of initial value problems with sDAEs

This paper provides an overview on numerical aspects in the simulation of differential-algebraic equations (DAEs). Amongst others we discuss the basic construction principles of frequently used discretization schemes, such as BDF methods, Runge-Kutta methods, and ROW methods, as well as their adaption to DAEs. Moreover, topics like consistent initialization, stabilization, parametric sensitivity analysis, co-simulation techniques, aspects of real-time simulation, and contact problems are covered. Finally, some illustrative numerical examples are presented.