| GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS |
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| 作者姓名： | 詹杰民 李毓湘 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金;教育部博士基金 |
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| 摘 要： | 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 Her-mite 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.
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| 关 键 词： | 有限光谱 方程式 流体动力学 计算数学 |
| 收稿时间： | 2005-05-15 |
| 修稿时间： | 2006-06-30 |
Generalized finite spectral method for 1D Burgers and KdV equations |
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| Jie-min Zhan,Yok-sheung Li.GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2006,27(12):1635-1643. |
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| Authors: | Jie-min Zhan Yok-sheung Li |
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| Institution: | 1. Department of Applied Mechanics and Engineering, Zhongshan University,Guangzhou,510275, P. R. China
2. Department of Civil and Structural Engineering, the Hong Kong Polytechnic University, Hong Kong, P. R. China |
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| 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 Her-mite 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. |
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| Keywords: | special orthogonal functions generalized finite spectral method nonlinear wave |
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