Abstract
In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L 2-norm. For the multi-interval spectral method in time, the L 2-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.
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