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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 1, Pages 81–96 (Mi zvmmf9638)  

This article is cited in 5 scientific papers (total in 5 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

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

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:1, 75–89

Bibliographic databases:

UDC: 519.62
Received: 22.04.2010
Revised: 04.07.2011

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Tropkina, “Parametrizatsiya medlennykh invariantnykh mnogoobrazii v modeli rasprostraneniya malyarii”, Vestn. SamGU. Estestvennonauchn. ser., 2012, no. 6(97), 66–74  mathnet
    2. M. O. Osintsev, V. A. Sobolev, “Reduction of dimension of optimal estimation problems for dynamical systems with singular perturbations”, Comput. Math. Math. Phys., 54:1 (2014), 45–58  mathnet  crossref  crossref  isi  elib  elib
    3. Mortell M.P. Shchepakina E. Sobolev V., “Singular Perturbations Introduction To System Order Reduction Methods With Applications Preface”: Shchepakina, E Sobolev, V Mortell, MP, Singular Perturbations: Introduction To System Order Reduction Methods With Applications, Lect. Notes Math., Lecture Notes in Mathematics, 2114, Springer-Verlag Berlin, 2014, IX+  mathscinet  isi
    4. A. A. Archibasov, A. Korobeinikov, V. A. Sobolev, “Asymptotic expansions of solutions in a singularly perturbed model of virus evolution”, Comput. Math. Math. Phys., 55:2 (2015), 240–250  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. V. A. Sobolev, E. A. Schepakina, E. A. Tropkina, “Parametrizatsiya invariantnykh mnogoobrazii medlennykh dvizhenii”, Vestn. SamU. Estestvennonauchn. ser., 24:4 (2018), 33–40  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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