Solving a Class of Near Index Problems as Perturbations of Index Problems

This paper extends a numerical algorithm of Chung and Westerberg for solving nonlinear index problems. The extension permits the solving of a special class of near index problems whose ill-conditioned behavior produces one or more small but nonzero pivots when attempting to solve the Newton equations corresponding to the model equations. Such problems are generally stiff differential-algebraic equation systems, sufficiently stiff that they often cannot be solved by existing stiff ordinary differential equation solvers such as LSODI. We present an algorithm for solving such problems both stably and accurately as a perturbation of the index problem which results from setting the small pivot(s) to 0.