Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems

作     者：Xuhong Yu Zhongqing Wang Huiyuan Li 

作者机构：University of Shanghai for Science and TechnologyShanghai 200093China State Key Laboratory of Computer Science/Laboratory of Parallel ComputingInstitute of SoftwareChinese Academy of SciencesBeijing 100190China 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2019年第1卷第2期

页      面：283-308页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China (Nos.11571238 11601332 91130014 11471312 and 91430216). 

主　　题：Generalized Jacobi polynomials Spectral method - Jacobi-Sobolev orthogonal basis functions Elliptic boundary value problems Error analysis 

摘      要：Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.