Why Standard Integration Packages Fail on a Near Index Problem

We examine the analytical behavior of a “near index” problem which Chung and Westerberg used as an example to illustrate their newly proposed algorithm for solving such problems. The example problem has both a stiff and an unstable component, the latter causing both implicit (in principle) and explicit (in practice because of round-off error) numerical methods to diverge when attempting to track its known finite solution. We explain why the numerical method of Chung and Westerberg, which corresponds to a perturbation expansion of the problem around the index problem to which it is close, has no difficulty in finding this solution.