## Abstract

We recall that the long-time behavior of the Kuramoto-Sivashinsky equation is the same as that of a certain finite system of ordinary differential equations. We show how a particular finite difference scheme approximating the Kuramoto-Sivashinsky may be viewed as a small C^{1} perturbation of this system for the grid spacing sufficiently small. As a consequence one may make deductions about how the global attractor and the flow on the attractor behaves under this approximation. For a sufficiently refined grid the long-time behavior of the solutions of the finite difference scheme is a function of the solutions at certain grid points, whose number and position remain fixed as the grid is refined. Though the results are worked out explicitly for the Kuramoto-Sivashinsky equation, the results extend to other infinite-dimensional dissipative systems.

Original language | English (US) |
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Pages (from-to) | 1155-1180 |

Number of pages | 26 |

Journal | Numerical Functional Analysis and Optimization |

Volume | 16 |

Issue number | 9-10 |

DOIs | |

State | Published - Jan 1 1995 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization