ON THE COMPUTATION OF IMPASSE POINTS OF QUASI-LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

We present computational algorithms for the calculation of impasse poi nts and higher-order singularities in quasi-linear differential-algebr aic equations. Our method combines a reduction step, transforming the DAE into a singular ODE, with an augmentation procedure inspired by nu merical bifurcation theory. Singularities are characterized by the van ishing of a scalar quantity that may be monitored along any trajectory . Two numerical examples with physical relevance are given.