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Title: Chebyshev finite spectral method with extended moving grids
Authors: Zhan, JM
Li, YS 
Dong, Z
Keywords: Chebyshev polynomial
finite spectral method
moving grid
non-uniform mesh
nonlinear wave
Issue Date: 2011
Publisher: Springer
Source: Applied mathematics and mechanics (English edition), 2011, v. 32, no. 3, p. 383-392 How to cite?
Journal: Applied mathematics and mechanics (English edition) 
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.
ISSN: 0253-4827
EISSN: 1573-2754
DOI: 10.1007/s10483-011-1423-6
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