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

Abstract

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 collocation method proposed, based on localized trial functions, provides a convenient numerical framework to develop approximate inertial manifolds in the case of partial differential problems (e.g. reaction/diffusion models) containing nonpolynomial nonlinearities. The collocation method is based on the interpolation of concentration/temperature fields by means of Gaussian–sinc functions. As model systems, we consider reaction diffusion schemes such as the non-isothermal model for stockpile ignition and the Elezgaray–Arneodo diffusion model.