| Legendre-Gauss-Lobatto节点的一个注记 |
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| 引用本文： | 王天军,殷政伟.Legendre-Gauss-Lobatto节点的一个注记[J].河南科技大学学报(自然科学版),2012(1):71-74,8,9. |
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| 作者姓名： | 王天军 殷政伟 |
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| 作者单位： | 河南科技大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金项目(10871131);河南省教育厅自然科学基金项目(2011B110014);河南科技大学博士启动基金项目(09001263),河南科技大学SRTP基金项目(2009179) |
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| 摘 要： | 以Legendre-Gauss-Lobatto点为节点的Lagrange插值基函数,构造N阶插值多项式P_N(x)。对P_N(x)分别求一阶和二阶导数,得到一阶和二阶微分矩阵。利用Legendre-Gauss-Lobatto点的性质导出一阶和二阶微分矩阵的关系,由此可利用Lagrange插值多项式数值求解微分方程。
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| 关 键 词： | Legendre-Gauss-Lobatto节点 Lagrange插值多项式 微分矩阵 |
A Note to Legendre-Gauss-Lobatto Nodes |
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| WANG Tian-Jun,YIN Zheng-Wei.A Note to Legendre-Gauss-Lobatto Nodes[J].Journal of Henan University of Science & Technology:Natural Science,2012(1):71-74,8,9. |
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| Authors: | WANG Tian-Jun YIN Zheng-Wei |
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| Institution: | (Mathematics & Statistics School,Henan University of Science & Technology,Luoyang 471003,China ) |
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| Abstract: | In this paper,Legendre-Gauss-Lobatto nodes were used to construct the N degree Lagrange interpolation polynomial P_N(x).First-order differentiation matrices and second order differentiation matrices were given by taking first-order derivative and second-order derivative of the P_N(x),respectively.The relations of the first-order differentiation matrices and second order differentiation matrices were derived by the properties of Legendre-Gauss-Lobatto nodes.It is much easier to approximate the solution of differential equations by Lagrange interpolation polynomial. |
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| Keywords: | Legendre-Gauss-Lobatto nodes Lagrange interpolation polynomial Differentiation matrices |
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