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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 1, Pages 81–96 (Mi zvmmf9638)  
This article is cited in 9 scientific papers (total in 9 papers)

Asymptotic expansions of slow invariant manifolds and reduction of chemical kinetics models

V. A. Soboleva, E. A. Tropkinab

a Samara State Aerospace University, Moskovskoe sh. 34, Samara, 443086 Russia
b Samara State University, ul. Akademika Pavlova 1, Samara, 443011 Russia
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Abstract: Methods of the geometric theory of singular perturbations are used to reduce the dimensions of problems in chemical kinetics. The methods are based on using slow invariant manifolds. As a result, the original system is replaced by one on an invariant manifold, whose dimension coincides with that of the slow subsystem. Explicit and implicit representations of slow invariant manifolds are applied. The mathematical apparatus described is used to develop N. N. Semenov’s fundamental ideas related to the method of quasi-stationary concentrations and is used to study particular problems in chemical kinetics.
Key words: integral manifolds, singular perturbations, iterative method, asymptotic expansion.
Received: 22.04.2010
Revised: 04.07.2011
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 1, Pages 75–89
DOI: https://doi.org/10.1134/S0965542512010125
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: V. A. Sobolev, E. A. Tropkina, “Asymptotic expansions of slow invariant manifolds and reduction of chemical kinetics models”, Zh. Vychisl. Mat. Mat. Fiz., 52:1 (2012), 81–96; Comput. Math. Math. Phys., 52:1 (2012), 75–89
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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