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

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• 作者：Wenjie Liu ; Jiebao Sun ; Boying Wu
• 关键词：Spectral method ; Block boundary value methods ; Semilinear parabolic equation ; Error estimate ; 65M12 ; 65M60 ; 65M70
• 刊名：Numerical Algorithms
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：71
• 期：2
• 页码：437-455
• 全文大小：528 KB
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• 作者单位：Wenjie Liu (1)
  Jiebao Sun (1)
  Boying Wu (1)
  
  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China
  
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Algorithms
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9265

文摘

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. Keywords Spectral method Block boundary value methods Semilinear parabolic equation Error estimate