Abstract
Our aim in this article is to study the implementation of the Nonlinear Galerkin Method in the context of pseudospectral (collocation) discretizations. We investigate the decomposition of a periodic function into its small and large scale components. The small scale component is requested to have only high modes and at the same time to be small in the physical space, at collocation points. This produces interesting connections between the physical space and the Fourier space representations of the function. An application is given to the Burgers equation and implementation issues are addressed.
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