Spectral methods in time for a class of parabolic partial differential equations

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In this paper, we introduce a fully spectral solution for the partial differential equation ut + uux + vuxx + μuxxx + λuxxxx = 0. For periodic boundary conditions in space, the use of Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. For all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time. © 1992 Academic Press, Inc. All rights reserved.

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Journal of Computational Physics