Numerical Algorithms

, Volume 71, Issue 2, pp 437–455 | Cite as

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

  • Wenjie Liu
  • Jiebao Sun
  • Boying Wu
Original Paper


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.


Spectral method Block boundary value methods Semilinear parabolic equation Error estimate 

Mathematical Subject Classifications (2010)

65M12 65M60 65M70 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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