  In this paper, we introduce a fictitious dynamics for describing the only
fast relaxation of a stiff ordinary differential equation (ODE) system towards
a stable low-dimensional invariant manifold in the phase-space (slow invariant
manifold - SIM). As a result, the demanding problem of constructing SIM of any
dimensions is recast into the remarkably simpler task of solving a properly
devised ODE system by stiff numerical schemes available in the literature. In
the same spirit, a set of equations is elaborated for local construction of the
fast subspace, and possible initialization procedures for the above equations
are discussed. The implementation to a detailed mechanism for combustion of
hydrogen and air has been carried out, while a model with the exact
Chapman-Enskog solution of the invariance equation is utilized as a benchmark.

Statistical Mechanics;Dynamical Systems