Generalized finite spectral method for 1D Burgers and KdV equations

Jie Min Zhan, Yok Sheung Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


A generalized finite spectral method is proposed. The method is of high-order accuracy. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Her-mite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection-diffusion problem) and KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.
Original languageEnglish
Pages (from-to)1635-1643
Number of pages9
JournalApplied Mathematics and Mechanics (English Edition)
Issue number12
Publication statusPublished - 1 Dec 2006


  • Generalized finite spectral method
  • Nonlinear wave
  • Special orthogonal functions

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Applied Mathematics

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