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 
Keywords: Special orthogonal functions
Generalized finite spectral method
Nonlinear wave
O351.2
O24
76M22
42C10
74J30
Issue Date: 2006
Publisher: Kluwer Academic Publishers
Source: Applied mathematics and mechanics, 2006, v. 27, no. 12, p. 1635-1643 How to cite?
Journal: Applied mathematics and mechanics 
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.
URI: http://hdl.handle.net/10397/27127
ISSN: 0253-4827
DOI: 10.1007/s10483-006-1206-z
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