The Interaction of System Structure, Index, and Numerical Stability in Classes of Differential/Algebraic Systems
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Systems which are difficult to solve numerically have always been considered to be ill-conditioned and their analysis has been somewhat neglected. Recent advances in DAE theory have established that, although high-index DAE systems pose some interesting challenges, they are not the anathema they were once thought to be. This paper will present several examples of DAE systems which arise in power systems and non-linear circuit analysis and will discuss both the analytical and numerical challenges these systems pose.