Determining nodes, finite difference schemes and inertial manifolds

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Abstract
The authors 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 they consider the 1D Kuramoto-Sivashinsky equation as a instructive paradigm. They remark that the results presented here apply to many other equations such as the 1D complex Ginzburg-Landau equation, the Chafee-Infante equation, etc.

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