Chebyshev-Gauss-Lobatto节点的一个注记  

An Annotation of Chebyshev-Gauss-Lobatto Node

作　　者：和文强[1] 秦国良[1] 包振忠 

机构地区：[1]西安交通大学流体机械研究所,陕西西安710049

出　　处：《郑州大学学报（理学版）》2015年第1期28-32,共5页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家重点基础研究发展计划(973计划)项目;编号2012CB026004

摘　　要：利用Lagrange插值基函数和Chebyshev多项式的性质,推导以Chebyshev-Gauss-Lobatto点为插值点构造的插值基函数的一阶、二阶微分矩阵的显示格式,并由插值点的性质得出两者之间的关系.通过对具有解析解的一维对流扩散方程进行数值求解,验证了一阶、二阶微分矩阵显式格式的正确性.数值结果表明:由微分矩阵显式格式可以方便地构造配置点谱方法中的拟谱算子,利用其求解微分方程,在较少的网格点时,即可得到快速收敛的高精度的数值结果.研究工作对配置点谱方法的应用具有一定的理论指导意义.The explicit formula of first-order and second-order differential matrix of interpolation function based on Chebyshev-Gauss-Lobatto node was deduced by taking advantage of the properties of Lagrange interpolation function and Chebyshev polynomial. The relationship between the two differential matrixes was obtained by using the characters of the interpolation node. The correctness of the explicit formula of the two differential matrixes was verified by the numerical solution of one-dimensional convection-diffusion equation. It was indicated that numerical results with high accuracy and fast convergence could be ob- tained by the use of fewer nodes when the spectral operator constructed by the explicit formula of the two differential matrixes was used to solve differential equation. The present study could be of theoretical im- portance to the application of collocation spectral method.

关 键 词：谱方法 Chebyshev-Gauss-Lobatto节点 Lagrange插值基函数 微分矩阵 

分 类 号：O368[理学—流体力学]