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Numerical solution of a nonlinear dissipative system using a pseudospectral method and inertial manifolds. (English) Zbl 0833.65087

A collocation method is introduced for computing approximate inertial manifolds. The method differs from the usual Galerkin methods in that the mapping from high to low Fourier modes is done in terms of values on fine and coarse grids.
The method is applied to the 1-dimensional Kuramoto-Sivashinsky equation. The authors conclude that the proposed method is more accurate than a comparable Galerkin approximation, but it is also more computationally expensive.

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure

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