Choosing a method for numerical integration

One-step algorithms have been developed and used by Prothero et al. [146, 166], Cdme et al. [156, 168], Pratt [177], Villadsen et al. [178] and Layokun and Slater [179]. Embedded semi-implicit Runge—Kutta algorithms have been discussed by Lapidus and co-workers [180]. 

The QSSA has been used, since Snow et al. [170, 171], by Goossens et al. [77—79] for their complex model of hydrocarbon pyrolysis. More recent versions of the QSSA are deduced from the theory of singular perturbation [118, 147—149, 156, 168, 173—175]. Asymptotic  

Other methods, which have not yet been used in chemical kinetics, include global or passive extrapolation (see Sect. 4.5.7), averaging methods, multistep, multiderivatives methods, exponential fitting and non-linear methods (see, for example, ref. 176 for references). 

Warner [176] has given a comprehensive discussion of the principal approaches to the solution of stiff differential equations, including a hundred references among the most pertinent books, papers and application packages directed at simulating kinetic models. Emphasis has been put not only on numerical and software problems such as robustness, improving the linear equation solvers, using sparse matrix techniques, etc., but also on the availability of a chemical compiler, i.e. a powerful interface between kineticist and computer. 

The problems of parametric estimation and model identification are among the most frequently encountered in experimental sciences and, thus, in chemical kinetics. Considerations about the statistical analysis of experimental results may be found in books on chemical kinetics and chemical reaction engineering [1—31], numerical methods [129—131, 133, 138], and pure and applied statistics [32, 33, 90, 91, 195—202]. The books by Kendall and Stuart [197] constitute a comprehensive treatise. A series of papers by Anderson [203] is of interest as an introductory survey to statistical methods in chemical engineering. Himmelblau et al. [204] have reviewed the methods for estimating the coefficients of ordinary differential equations which are linear in the 

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