| 四阶方程两点边值问题Hermite有限元解的渐近展式与外推 |
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| 引用本文： | 王奇生,邓康. 四阶方程两点边值问题Hermite有限元解的渐近展式与外推[J]. 高等学校计算数学学报, 2006, 28(4): 299-306 |
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| 作者姓名： | 王奇生 邓康 |
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| 作者单位： | 1. 湘潭大学数学与计算科学学院,湘潭,411105;南华大学数理学院,衡阳,421001
2. 湖南科技大学数学与计算科学学院,湘潭,411201 |
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| 基金项目： | 作者衷心地感谢黄云清教授,舒适教授所给予的许多有益的建议. |
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| 摘 要： | 1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上．许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧．本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式．考虑四阶方程两点边值问题
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| 关 键 词： | Richardson外推 Hermite 两点边值问题 渐近展式 有限元解 四阶方程 嵌入定理 微分方程 |
| 收稿时间： | 2004-06-16 |
| 修稿时间： | 2004-06-16 |
THE ASYMPTOTIC EXPANSIONS OF THE HERMITE FINITE ELEMENT APPROXIMATIONS FOR TWO POINT BOUNDARY VALUE PROBLEM OF FOURTH-ORDER DIFFERENTIAL EQUATIONS WITH EXTRAPOLATION |
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| Wang Qisheng,Deng Kang. THE ASYMPTOTIC EXPANSIONS OF THE HERMITE FINITE ELEMENT APPROXIMATIONS FOR TWO POINT BOUNDARY VALUE PROBLEM OF FOURTH-ORDER DIFFERENTIAL EQUATIONS WITH EXTRAPOLATION[J]. Numerical Mathematics A Journal of Chinese Universities, 2006, 28(4): 299-306 |
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| Authors: | Wang Qisheng Deng Kang |
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| Abstract: | In this paper, the Hermite finite element approximation for two-point boundary value problem of fourth-order differential equation is discussed. We not obtain only the asymptotic expansions by the method of energy embedment as following: uh(xi)=u(xi) h4W(xi) O(h6),but also the formulas of the Richardson extrapolation. An analogous expansion also holds for uh"(x)-the average of the second order derivative of the approximate solution. |
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| Keywords: | fourth-order equations Hermite finite element energy embedment method asymptotic expansions Richardson extrapolation. |
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