| 常微分方程初值问题连续有限元的超收敛性 |
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| 引用本文： | 杨禄源,汤琼. 常微分方程初值问题连续有限元的超收敛性[J]. 高等学校计算数学学报, 2004, 26(1): 91-96 |
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| 作者姓名： | 杨禄源 汤琼 |
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| 作者单位： | 株洲工学院信息与计算科学系,株洲,412008;株洲工学院信息与计算科学系,株洲,412008 |
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| 基金项目： | 国家自然科学基金(10361003)，桂林电子工业学院博士基金(Z20306) |
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| 摘 要： | 1 引言及算法 考虑一阶非线性常微分方程初值问题u′=f(t,u),t∈I=[0,T],u(0)=u_0,(1)其中f(t,u)是t,u的适当光滑函数。我们知道,常微分方程初值问题的数值解法不仅本身有独立的兴趣,它也是抛物与双曲方程时间离散的基础。目前已有许多数值方法,如
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| 关 键 词： | 常微分方程 初值问题 连续有限元 超收敛性 光滑函数 |
SUPERCONVERGENCE IN CONTINUOUS FINITE ELEMENTS FOR INITIAL VALUE PROBLEM OF ORDINARY DIFFERENTIAL EQUATION |
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| Yan Luyuan Tang Qiong. SUPERCONVERGENCE IN CONTINUOUS FINITE ELEMENTS FOR INITIAL VALUE PROBLEM OF ORDINARY DIFFERENTIAL EQUATION[J]. Numerical Mathematics A Journal of Chinese Universities, 2004, 26(1): 91-96 |
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| Authors: | Yan Luyuan Tang Qiong |
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| Abstract: | In this paper, n-degree continuous finite element approximation to an initial value problem of nonlinear ordinary differential equation is discussed. An optimal superconvergence u-uh-O(h2n) at node points and u-uh= O(hn+2),n > 2, at Lobatto points in each element respectively is proved. When continuous finite element method is applied to nonlinear Schrodinger equation, a conservation Law is obtained. |
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| Keywords: | ordinary differential equation Initial value problem continuous finite element superconvergence conservation law. |
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