## A generalized steady state approximation for the numerical solution of sets of ordinary differential equations with widely differing time constants |

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### Contents

GENERAL NATURE OF THE STEADY STATE | 21 |

IMPLEMENTATION OF THE GENERALIZED STEADY STATE PROCEDURE | 43 |

CONCLUDING REMARKS | 96 |

8 other sections not shown

### Common terms and phrases

accuracy Appendix applied assumed asymptotic expansions behavior calculations Chapter characteristic Chemical Kinetics chemical system CM rH coefficient matrix Combustion considered dependent variables determined diagonal terms element conservation enthalpy equa equation 3.1 equilibrium error checks error growth estimate Euler method exact solution exponential Friedlander and Seinfeld Hence hydrogen hydrogen-air system inner region inner solution intermediate concentrations iterative procedure Keck and Gillespie linear differential equations linear equations Lomax and Bailey mass fractions mediates method of matched molecular Moretti negative concentrations number of intermediates Numerical Integration numerical solution obtained ordinary differential equations outer series solution over-all parameter photochemical smog potential intermediates rate constants ratio reactants requires rH CM rH rH Runge-Kutta method set of intermediates shown in Figure smallest solu species concentrations stability steady state approximation steady state concentrations steady state error steady state method stiff equations Stoichiometric Hydrogen-Air Reaction technique temperature time-rate-of-change equations tion truncation error yields zero