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A preceding paper demonstrated that explicit asymptotic methods generallywork much better for extremely stiff reaction networks than has previously beenshown in the literature. There we showed that for systems well removed fromequilibrium explicit asymptotic methods can rival standard implicit codes inspeed and accuracy for solving extremely stiff differential equations. In thispaper we continue the investigation of systems well removed from equilibrium byexamining quasi-steady-state (QSS) methods as an alternative to asymptoticmethods. We show that for systems well removed from equilibrium, QSS methodsalso can compete with, or even exceed, standard implicit methods in speed, evenfor extremely stiff networks, and in many cases give somewhat betterintegration speed than for asymptotic methods. As for asymptotic methods, wewill find that QSS methods give correct results, but with non-competitiveintegration speed as equilibrium is approached. Thus, we shall find that bothasymptotic and QSS methods must be supplemented with partial equilibriummethods as equilibrium is approached to remain competitive with implicitmethods.

Explicit Integration of Extremely-Stiff Reaction Networks: Quasi-Steady-State Methods