A general analysis of approximate nonlinear lumping in chemical kinetics. I. Unconstrained lumping
- Department of Chemistry, Princeton University, Princeton, New Jersey 08540 (United States)
- Department of Computer Science, Agricultural Engineering Faculty, University of Agricultural Science, H-2103 Goedoello, Pater K. u. 1 (Hungary)
A general analysis of approximate nonlinear lumping for a chemical kinetic system described by an [ital n]-dimensional first order ordinary differential equation system [ital d][bold y]/[ital dt]=[bold f]([bold y]) is presented. There is a one-to-one relation between the differential equation system and the linear partial differential operator [ital A]=[summation][sup [ital n]][sub [ital i]=1][ital f][sub [ital i]]([bold y])([partial derivative]/[partial derivative][ital y][sub [ital i]]). The algebraic method in nonlinear perturbation theory is utilized to approximately transform [ital A] into some canonical forms in which the new dependent variables are partly separated. These canonical forms of [ital A] will give the generalized eigenfunctions or other higher dimensional unconstrained nonlinear lumping schemes of the original system approximately. Unconstrained nonlinear lumping gives a reduced differential equation system describing new variables which are nonlinear functions of the original ones. This approach may supply some purely fast variables. The solutions of original dependent variables can be obtained by the inverse transformation from the lumped variables and the approximate analytical solutions of the purely fast variables. The theoretical basis of this approach is presented. A simple example is used for illustration.
- OSTI ID:
- 7107323
- Journal Information:
- Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 101:2; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
CHEMICAL REACTION KINETICS
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
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FUNCTIONS
KINETICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
REACTION KINETICS
TRANSFORMATIONS