Wavelet-like collocation method for finite-dimensional reduction of distributed systems

A wavelet-like collocation method is proposed to approach the reduction of dissipative distributed systems, expressed by means of partial differential equations, applying the methods of inertial manifold theory. The collocati on method proposed, based on localized trial functions, provides a convenie nt numerical framework to develop approximate inertial manifolds in the cas e of partial differential problems (e.g. reaction/diffusion models) contain ing nonpolynomial nonlinearities. The collocation method is based on the in terpolation of concentration/temperature fields by means of Gaussian-sine f unctions. As model systems, we consider reaction diffusion schemes such as the non-isothermal model for stockpile ignition and the Elezgaray-Ameodo di ffusion model. (C) 2000 Elsevier Science Ltd. All rights reserved.