Low-Dimensional Galerkin Approximations of Nonlinear Delay Differential Equations

@article{Chekroun2015LowDimensionalGA,
  title={Low-Dimensional Galerkin Approximations of Nonlinear Delay Differential Equations},
  author={Micka{\"e}l D. Chekroun and Michael Ghil and Honghu Liu and Shouhong Wang},
  journal={arXiv: Chaotic Dynamics},
  year={2015}
}
This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point mass, and introduce polynomials orthogonal with respect to such an inner product that live in the domain of the linear operator associated with the underlying DDE. These polynomials are then used to design a general Galerkin scheme for which we derive… 

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