Applied Mathematics and Mechanics

, Volume 17, Issue 4, pp 373–378 | Cite as

Spectral method in time for KdV equations

  • Wu Shengchang
  • Liu Xiaoqing


This paper presents a fully spectral discretization method for solving KdV equations with periodic boundary conditions: Chebyshev pseudospectral approximation in the time direction and Fourier Galerkin approximation in the spatial direction. The expansion coefficients are determined by minimizing an object functional. Rapid convergence of the method is proved.

Key words

KdV equation spectral method Galerkin approximation pseudospectral approximation 


  1. [1]
    B. C.Jiang, et al., Spectral Methods in Computational Physics, Hunan Science and Technology Press, Changsha, (1989) (in Chinese)Google Scholar
  2. [2]
    G.Ierley, et al., Spectral methods in time for a class of parabolic partial differential equations, J. Comp. Phys., 102 (1992), 88–97.Google Scholar
  3. [3]
    R. K.Dodd, Solitons and Nonlinear Wave Equations, Academic Press, London (1982).Google Scholar
  4. [4]
    D. R. Wang, Methods for Solving Nonliear Equations and Optimization Methods, People's Education Press, (1979). (in Chinese)Google Scholar
  5. [5]
    R. G.Voigt, et al., Spectral Method for PDE, SIAM Philadelpia (1984).Google Scholar
  6. [6]
    C.Canuto, et al., Analysis of the combinated finite element and Fourier interpolation, Numer. Math., 39 (1982), 205–220.Google Scholar
  7. [7]
    D. Q. Li, et al., Nonlinear Evolutional Equations, Science Press, (1980). (in Chinese)Google Scholar
  8. [8]
    P.Dutt, Spectral methods for initial boundary value problem — an alternative approach, SIAM J. Numer. Anal., 27, 4 (1990), 885–903.Google Scholar
  9. [9]
    D. Gottlieb, Numerical analysis of spectral method, CBMS-NSF, Regional Conference Series in Applied Math., 26 (1977)Google Scholar
  10. [10]
    R. A. Adams, Sobolev Spaces, Academia Press (1975).Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Wu Shengchang
    • 1
    • 2
  • Liu Xiaoqing
    • 1
    • 2
  1. 1.Institute of Applied MathematicsAcademic SinicaBeijingP. R. China
  2. 2.Laboratory of Management Decison and Information SystemsAcademia SinicaBeijingP. R. China

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