This article is cited in 10 papers

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

V. A. Sobolev^a, E. A. Tropkina<sup>b

a</sup> 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.

UDC: 519.62

Received: 22.04.2010
Revised: 04.07.2011

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

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•