Linear index-1 DAEs: Regular and singular problems
The authors study linear time-varying differential algebraic equations. They start by reviewing and comparing reduction methods with projector techniques in the regular index-1 case and propose a new hybrid approach. As examples they mainly use systems coming from the simulation of electrical circuits. Then they move on to singular problems distinguishing two types of singularities on the basis of the properties of certain system matrices. Their main tool is a scalarly implicit reduced ordinary differential equation which becomes singular, if the original differential-algebraic equation possesses singularities. Special emphasis is put on making as few smoothness assumptions as possible.
scientific article; zbMATH DE number 2153908