Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/27127
Title: Generalized finite spectral method for 1D burgers and KdV equations
Authors: Zhan, JM
Li, YS 
Issue Date: 2006
Source: Applied mathematics and mechanics (English edition), 2006, v. 27, no. 12, p. 1635-1643
Abstract: 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 Hermite 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.
Keywords: Special orthogonal functions
Generalized finite spectral method
Nonlinear wave
O351.2
O24
76M22
42C10
74J30
Publisher: Springer
Journal: Applied mathematics and mechanics (English edition) 
ISSN: 0253-4827
EISSN: 1573-2754
DOI: 10.1007/s10483-006-1206-z
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