Applied Mathematics and Mechanics

, Volume 24, Issue 10, pp 1168–1183 | Cite as

Analysis of chebyshev pseudospectral method for multi-dimensional generalized srlw equations

  • Shang Ya-dong
  • Guo Bo-ling


The Chebyshev pseudospectral approximation of the homogenous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discrete Chebyshev pseudospectral scheme is constructed. The convergence of the approximation solution and the optimum error of approximation solution are obtained.

Key words

multi-dimensional generalized SRLW equation initial and boundary value problem Chebyshev pseudospectral method error estimate 

Chinese Library Classification number


2000 Mathematics Subject Classification

65M70 65N30 


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  1. [1]
    Seyler C E, Fanstermacler D C. A symmetric regularized long wave equation[J].Phys Fluids, 1984,27(1):4–7.MATHCrossRefGoogle Scholar
  2. [2]
    Iskandar L, Jain P C. Numerical solutions of the improved Boussinesq equation[J].Proc Indian Acad Sci Math Sci, 1980,89(1):171–181.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Soerensen M P, Christainsen P L, Lomdahl P S. Solitary waves on nonlinear elastic rods[J].J Acoust Soc Amer, 1984,76(5):871–879.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Bogolubsky J L. Some examples of inelastic soliton interaction[J].Comput Phys Comm, 1977,13 (1):149–155.CrossRefGoogle Scholar
  5. [5]
    CHEN Lin. Stability and instability of solitary waves for generalized symmetric regularized long wave equations[J].Physica D, 1998,118(1/2):53–68.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    GUO Bo-ling. The spectral method for symmetric regularized wave equations[J].J Comput Math, 1987,5(4):297–306.MathSciNetGoogle Scholar
  7. [7]
    ZHENG Jia-dong, ZHANG Ru-fen, GUO Ben-yu. The Fourier pseudo-spectral method for SRLW equation [J].Applied Mathematics and Mechanics (English Edition), 1989,10(9):843–852.MathSciNetCrossRefGoogle Scholar
  8. [8]
    ZHENG Jia-dong. The pseudospectral collocation method for the generalized SRLW equations[J].Numer Math Sinica, 1989,11(1):64–72. (in Chinese)Google Scholar
  9. [9]
    GUO Bo-ling. The existence of global solutions and “blow up” phenomena for a system of multidimensional symmetric regularized weve equations [J].Acta Math Appl Sinica, 1992,8(1):59–72.MathSciNetCrossRefGoogle Scholar
  10. [10]
    SHANG Ya-dong, LIZ hi-shen. The Fourier spectral methods for solving the multidimensional generalized symmetric regularized long wave equations [J].Mumer Math-A Journal of Chinese University, 1988,21(1):48–60. (in Chinese)Google Scholar
  11. [11]
    MA He-ping, GUO Ben-yu. The Chebyshev spectral methods for Burgers-like equations[J].J Comput Math, 1988,6(1):51–56.Google Scholar
  12. [12]
    Bressan N, Quarteroni A. Analysis of Chebyshev collocation methods for parabolic equations[J].SIAM J Numer Anal, 1986,23(6):1138–1154.MATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    Canuto C, Hussaini M Y, Quarteroni A,et al. Spectral Methods in Fluid Dynamics[M]. New York: Springer-Verlag, 1988.Google Scholar
  14. [14]
    XIANG Xin-ming, ZHANG Fa-yong. Chebyshev pseudospectral method for the generalized BBM equations in higher dimension [J].Numer Math Sinica, 1991,13(4):403–411. (in Chinese)Google Scholar
  15. [15]
    GUO Ben-yu.Spectral Methods and Their Applications[M]. Singapore: World Scientific, 1998.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanic 2003

Authors and Affiliations

  • Shang Ya-dong
    • 1
  • Guo Bo-ling
    • 2
  1. 1.Department of MathematicsGuangzhou UniversityGuangzhouP.R.China
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingP.R.China

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