Fourier Collocation Splittings for Partial Differential Equations

In this article we study computational issues related to a nonlinear Galerkin type splitting (NLG) of partial differential equations in the case of a Fourier collocation discretization. We present an extension of the method to two-dimensional problems and show that the sole separation of modes in NLG can bring precision and computational costs advantages to the standard collocation scheme. Numerical experiments with the Burgers and a reaction-diffusion equation for 1 and 2 dimensions are also shown.

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