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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.
We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends on whethe
In two preceding papers we have shown that, when reaction networks are well-removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically-stabilized integration schemes that rival standard implicit methods
In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the numerical inte
We discuss the numerical solution methods available when solving for the steady-state density matrix of a time-independent open quantum optical system, where the system operators are expressed in a suitable basis representation as sparse matrices. In
A brief historical account of modern cosmology shows that the standard big bang (BB) model, believed by so many, does not have the strong observational foundations that are frequently claimed for it. The theory of the Quasi-Steady State Cosmology (QS