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Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

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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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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200436, P.R. China

    Jian-guo Tang

  2. Department of Mathematics, Lingling College, Yongzhou Hunan, 425006, P.R. China

    Jian-guo Tang

  3. Department of Mathematics, Shanghai University, Shanghai, 200436, P.R. China

    He-ping Ma

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  1. Jian-guo Tang
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  2. He-ping Ma
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Tang, Jg., Ma, Hp. Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations. Advances in Computational Mathematics 17, 349–367 (2002). https://doi.org/10.1023/A:1016273820035

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