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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (10): 1255-1268.doi: https://doi.org/10.1007/s10483-011-1498-9

• Articles • 上一篇    下一篇

Multidomain pseudospectral methods for nonlinearn convection-diffusion equations

纪园园1 吴华1 马和平1 郭本瑜2   

  1. 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, Mathematical and Science College, Shanghai Normal University, Shanghai 200234, P. R. China
  • 收稿日期:2011-05-18 修回日期:2011-06-28 出版日期:2011-10-09 发布日期:2011-10-09

Multidomain pseudospectral methods for nonlinear convection-diffusion equations

JI Yuan-Yuan1, Wu Hua1, MA He-Ping1, GUO Ben-Yu2   

  1. 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, Mathematical and Science College, Shanghai Normal University, Shanghai 200234, P. R. China
  • Received:2011-05-18 Revised:2011-06-28 Online:2011-10-09 Published:2011-10-09

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摘要： 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.

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.

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