| 三阶微分方程的多区域Legendre-Petrov-Galerkin谱方法 |
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| 引用本文： | 王振华,马和平. 三阶微分方程的多区域Legendre-Petrov-Galerkin谱方法[J]. 应用数学与计算数学学报, 2011, 25(1): 11-19 |
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| 作者姓名： | 王振华 马和平 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | 国家自然科学基金资助项目，上海市教委重点学科建设资助项目 |
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| 摘 要： | 提出三阶微分方程初边值问题的多区域Legendre-Petrov-Galerkin谱方法.对于三阶线性微分方程,证明该方法全离散格式的稳定性,并给出L~2-误差估计.进而将该方法和Legendre配置方法相结合,应用于某些非线性问题.数值算例对单区域和多区域方法的结果进行比较.
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| 关 键 词： | 多区域Legendre-Petrov-Galerkin谱方法 三阶微分方程 Legendre配置方法 |
A multidomain Legendre-Petrov-Galerkin spectral method for third-order differential equations |
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| WANG Zhen-hua,MA He-ping. A multidomain Legendre-Petrov-Galerkin spectral method for third-order differential equations[J]. Communication on Applied Mathematics and Computation, 2011, 25(1): 11-19 |
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| Authors: | WANG Zhen-hua MA He-ping |
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| Affiliation: | WANG Zhen-hua,MA He-ping (College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | A multidomain Legendre-Petrov-Galerkin spectral method for third-order differential equations with initial boundary conditions is considered.The method is firstly applied to the linear third-order differential equations.The stability and the rate of convergence are proved.Numerical results are given for both the single domain and the two domain methods to make a comparison.Also,it is generalized to to some nonlinear problems with the Legendre collocation.Numerical results show the accuracy and efficiency of the method. |
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| Keywords: | multidomain Legendre-Petrov-Galerkin spectral method third-order differential equation Legendre collocation method |
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