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Spectral methods in time for a class of parabolic partial differential equations. (English) Zbl 0758.65064
The authors propose a fully spectral solution for the equation \(u_ t+uu_ x+au_{xx}+bu_{xxx}+cu_{xxxx}=0\) using a Fourier expansion in \(x\) and a Chebyshev expansion in \(t\).

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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