Abstract
For solving Burgers' equation with periodic boundary conditions, this paper presents a fully spectral discretization method: Fourier Galerkin approximation in the spatial direction and Chebyshev pseudospectral approximation in the time direction. The expansion coefficients are determined by means of minimizing an object functional, and rapid convergence of the method is proved.
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Wu, S., Liu, X. Convergence of spectral method in time for Burgers' equation. Acta Mathematicae Applicatae Sinica 13, 314–320 (1997). https://doi.org/10.1007/BF02025886
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DOI: https://doi.org/10.1007/BF02025886