Chebyshev finite spectral method with extended moving grids

Jie Min Zhan, Yok Sheung Li, Zhi Dong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

A Chebyshev finite spectral method on non-uniform meshes is proposed. An equidistribution scheme for two types of extended moving grids is used to generate grids. One type is designed to provide better resolution for the wave surface, and the other type is for highly variable gradients. The method has high-order accuracy because of the use of the Chebyshev polynomial as the basis function. The polynomial is used to interpolate the values between the two non-uniform meshes from a previous time step to the current time step. To attain high accuracy in the time discretization, the fourth-order Adams-Bashforth- Moulton predictor and corrector scheme is used. To avoid numerical oscillations caused by the dispersion term in the Korteweg-de Vries (KdV) equation, a numerical technique on non-uniform meshes is introduced. The proposed numerical scheme is validated by the applications to the Burgers equation (nonlinear convectiondiffusion problems) and the KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparisons. Numerical results agree very well with the corresponding analytical solutions in all cases.
Original languageEnglish
Pages (from-to)383-392
Number of pages10
JournalApplied Mathematics and Mechanics (English Edition)
Volume32
Issue number3
DOIs
Publication statusPublished - 1 Mar 2011

Keywords

  • Chebyshev polynomial
  • finite spectral method
  • moving grid
  • non-uniform mesh
  • nonlinear wave

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanics of Materials
  • Mechanical Engineering

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