Collocation Methods and Inertial Manifold Theory for the Modal Reduction of Dissipative Distributed Systems

Abstract

A collocation method is proposed to approach the reduction of dissipative distributed systems through application of the methods of Inertial Manifold theory. The collocation method proposed provides a numerical framework to develop approximate inertial manifolds (AIMs) in the case of partial differential problems (e.g. reaction/diffusion models) containing non-polynomial nonlinearities. The collocation method is also the starting point for the alternative construction of AIMs by means of a renormalization approach naturally derived from the incremental unknown method developed by Temam in a finite difference framework.