Generalized Jacobi-Gauss-Lobatto interpolation  

作　　者：Zhengsu WAN Benyu GUO Chengjian ZHANG 

机构地区：[1]School of Mathematics and Statistics, Huazhong University of Science and Technology,Wuhan 430074, China [2]Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006,China [3]Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

出　　处：《Frontiers of Mathematics in China》2013年第4期933-960,共28页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171125, 11271118, 91130003）, the National Natural Science Foundation of China （Tianyuan Fund for Mathematics, Grant No. 11226170）, the Natural Science Foundation of Hunan Province （Grant No. 13JJ4095）, the Postdoctoral Foundation of China （Grant No. 20100471182）, the Construct Program of the Key Discipline in Hunan Province, and the Key Foundation of Hunan Provincial Education Department （Grant No. 11A043）.

摘　　要：We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.

关 键 词：Generalized Jacobi-Gauss-Lobatto interpolation pseudospectral method non-uniformly weighted Sobolev space 

分 类 号：O241.3[理学—计算数学] TB115[理学—数学]