DETERMINING NODES, FINITE-DIFFERENCE SCHEMES AND INERTIAL MANIFOLDS
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The aim of this paper is to present a connection between the concepts of determining nodes and inertial manifolds with that of finite difference and finite volumes approximations to dissipative partial differential equations. In order to illustrate this connection we consider the id Kuramoto-Sivashinsky equation as a instructive paradigm. We remark that the results presented here apply to many other equations such as the d complex Ginzburg-Landau equation, the Chafee-Infante equation, etc. 1991 IOP Publishing Ltd and LMS Publishing Ltd.
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