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Multidomain pseudospectral methods for nonlinear convection-diffusion equations

  • Yuan-yuan Ji (纪园园)
  • Hua Wu (吴华)
  • He-ping Ma (马和平)Email author
  • Ben-yu Guo (郭本瑜)
Article

Abstract

Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method, but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.

Key words

multidomain Legendre/Chebyshev collocation convection-diffusion equation 

Chinese Library Classification

O241.82 

2010 Mathematics Subject Classification

65M70 35L65 35L50 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yuan-yuan Ji (纪园园)
    • 1
  • Hua Wu (吴华)
    • 1
  • He-ping Ma (马和平)
    • 1
    Email author
  • Ben-yu Guo (郭本瑜)
    • 2
  1. 1.Department of Mathematics, College of SciencesShanghai UniversityShanghaiP. R. China
  2. 2.Department of Mathematics, Mathematical and Science CollegeShanghai Normal UniversityShanghaiP. R. China

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