Legendre-Gauss-Lobatto节点的一个注记  

A Note to Legendre-Gauss-Lobatto Nodes

作　　者：王天军[1] 殷政伟[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2012年第1期71-74,8-9,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：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)

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。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.

关 键 词：Legendre—Gauss—Lobatto节点 LAGRANGE插值多项式 微分矩阵 

分 类 号：O175.2[理学—数学]