title: Single and multi-interval Legendre tau -methods in time for parabolic equations
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 methods in time. For the single interval spectral method in time, we obtain the optimal error estimate in L/sup 2/-norm. For the multi-interval spectral method in time, the L/sup 2/-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods
keyphrases: parabolic equation periodic boundary conditions Fourier approximation Legendre Petrov-Galerkin method interval spectral method optimal error estimation interval decomposition error analysis partial differential equations