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A general algorithm for improving ILDMs

The method of intrinsic low-dimensional manifolds (ILDMs) has proven to be an efficient tool for the simplification of chemical kinetics. Nevertheless, there are still some open questions with respect to an efficient calculation and implementation of ILDMs. In this paper, we focus on the efficient calculation of ILDMs and present a refinement method for ILDMs. The method is based on an evolution equation of the manifolds towards a steady state solution which then represents the slow manifold. It has the property that it is continuous, differentiable, and in addition, it is an inertial manifold which represents the slow dynamics of the chemical system. In this way, many of the problems associated with the concept of ILDM are overcome.