Invariant grids for reaction kinetics

Details Invariant grids for reaction kinetics Invariant grids for reaction kinetics

2003-07-03

arxiv.org/abs/cond-mat/0307076v1

Physica A, Volume 333, 15 February 2004, Pages 106-154

Physics

Condensed Matter

Materials Science

53 pages, 8 jpg figures

Scientific paper

10.1016/j.physa.2003.10.043

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, {\it 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.

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