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Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations

Published: 01 February 2016 Publication History

Abstract

In this paper, we present a high-order accurate method for two-dimensional semilinear parabolic equations. The method is based on a Galerkin-Chebyshev spectral method for discretizing spatial derivatives and a block boundary value methods of fourth-order for temporal discretization. Our formulation has high-order accurate in both space and time. Optimal a priori error bound is derived in the weighted L 2$L^{2}_{\omega }$-norm for the semidiscrete formulation. Extensive numerical results are presented to demonstrate the convergence properties of the method.

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        Published In

        cover image Numerical Algorithms
        Numerical Algorithms  Volume 71, Issue 2
        February 2016
        242 pages

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        Springer-Verlag

        Berlin, Heidelberg

        Publication History

        Published: 01 February 2016

        Author Tags

        1. 65M12
        2. 65M60
        3. 65M70
        4. Block boundary value methods
        5. Error estimate
        6. Semilinear parabolic equation
        7. Spectral method

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