A. N. Gorban, I. V. Karlin, A. Yu.Zinovyev
Invariant grids for reaction kinetics
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ABSTRACT.  In this paper, we review the construction of low-dimensional manifolds of reduced description for 
equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is 
based on a formulation of the condition of invariance as an equation, and its solution by Newton 
iterations. A grid-based version of MIM is developed. Generalizations to open systems are suggested. 
The set of methods covered makes it possible to effectively reduce description in chemical kinetics. 
The most essential new element of this paper is the systematic consideration of a discrete analogue 
of the slow (stable) positively invariant manifolds for dissipative systems, invariant grids. 
We describe the Newton method and the relaxation method for the invariant grids construction. The 
problem of the grid correction is fully decomposed into the problems of the grid's nodes correction. 
The edges between the nodes appears only in the calculation of the tangent spaces. This fact 
determines high computational efficiency of the invariant grids method.