| 变系数Burgers方程的一种预处理谱方法 |
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| 引用本文： | 邓芳芳,马和平,曾凡海. 变系数Burgers方程的一种预处理谱方法[J]. 应用数学与计算数学学报, 2010, 24(1): 99-106 |
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| 作者姓名： | 邓芳芳 马和平 曾凡海 |
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| 作者单位： | 上海大学数学系,上海,200444 |
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| 基金项目： | 国家自然科学基金项目，上海市教委重点学科建设项目 |
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| 摘 要： | 本文用预处理Legendre-Galerkin-Chebyshev配置方法来求解二阶变系数Burgers方程,该方法首先对方程进行预处理,然后在空间方向应用Legendre-Galerkin-Chebyshev配置方法,对时间方向采用leap-frog/Crank-Nicolson格式进行离散,这样可使得变系数项和非线性项能够显式计算.我们对该方法进行了误差估计,并通过数值算例验证了算法的有效性和理论分析的正确性.
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| 关 键 词： | Legendre-Galerkin-Chebyshev配置方法 预处理 变系数 |
| 收稿时间： | 2010-03-15 |
Spectral Method for Second-order Nonlinear Evolution Equations with Variable Coefficients |
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| Deng Fangfang,Ma Heping,Zeng Fanhai. Spectral Method for Second-order Nonlinear Evolution Equations with Variable Coefficients[J]. Communication on Applied Mathematics and Computation, 2010, 24(1): 99-106 |
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| Authors: | Deng Fangfang Ma Heping Zeng Fanhai |
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| Affiliation: | Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | In this paper, a preconditioning Legendre-Galerkin-Chebyshev collocation method is developed for the second-order Burgers equation with variable coefficient. First, the form of the equation is changed by the idea of the preconditioning method. Then we apply the Legendre-Galerkin-Chebyshev collocation method to the changed equation. For the time discretization, we adopt the leap-frog/Crank-Nicolson scheme such that the nonlinear and variable-coefficient terms can be dealt with explicitly. Error analysis is given to this method. The numerical results are given to confirm the validity of the scheme and the correctness of theoretical analysis. |
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| Keywords: | Legendre-Galerkin-Chebyshev-collocation preconditioning variable coefficient |
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