A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from equilibrium explicit asymptotic methods can rival standard implicit codes in speed and accuracy for solving extremely stiff differential equations. In this paper we continue the investigation of systems well removed from equilibrium by examining quasi-steady-state (QSS) methods as an alternative to asymptotic methods. We show that for systems well removed from equilibrium, QSS methods also can compete with, or even exceed, standard implicit methods in speed, even for extremely stiff networks, and in many cases give somewhat better integration speed than for asymptotic methods. As for asymptotic methods, we will find that QSS methods give correct results, but with non-competitive integration speed as equilibrium is approached. Thus, we shall find that both asymptotic and QSS methods must be supplemented with partial equilibrium methods as equilibrium is approached to remain competitive with implicit methods.
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