GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

• Published in: Applied mathematics and mechanics Vol. 27; no. 12; pp. 1635 - 1643
• Main Author: 詹杰民 李毓湘
• Format: Journal Article
• Language: English
• Published: Department of Applied Mechanics and Engineering, Zhongshan University,Guangzhou,510275, P. R. China%Department of Civil and Structural Engineering, the Hong Kong Polytechnic University, Hong Kong, P. R. China 01-12-2006
• Subjects: Accuracy; Burgers equation; Dispersions; Hermite polynomials; Mathematical analysis; Mathematical models; Oscillations; Spectral methods; 方程式; 有限光谱; 流体动力学; 计算数学; special orthogonal functions; generalized finite spectral method; nonlinear wave
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-006-1206-z

A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-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.