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 \(L^{2}_{\omega }\)-norm for the semidiscrete formulation. Extensive numerical results are presented to demonstrate the convergence properties of the method.
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Liu, W., Sun, J. & Wu, B. Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations. Numer Algor 71, 437–455 (2016). https://doi.org/10.1007/s11075-015-0002-x
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DOI: https://doi.org/10.1007/s11075-015-0002-x