Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations |
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Authors: | Wenjie Liu Jiebao Sun Boying Wu |
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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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