Internal Dynamics Stability of a Heat Conduction System Reduced via Orthogonal Collocation

Abstract

This paper deals with the crucial problem of choice of the collocation points in the reduction of a one-dimensional heat transfer problem into an ordinary differential equation system. It is shown that, for its parabolic differential equation, the use of such an approach can either lead to systems with or without a NMP behaviour, which is not characteristic of the original behaviour of the initial system. A simple rule of choice, restrained to this class of systems, is given to avoid this phenomenon.