Jacobi-Sobolev Orthogonal Polynomials and Spectral Methods for Elliptic Boundary Value Problems

doi:10.1007/s42967-019-00016-x

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (2): 283-308.doi: 10.1007/s42967-019-00016-x

Jacobi-Sobolev Orthogonal Polynomials and Spectral Methods for Elliptic Boundary Value Problems

Xuhong Yu¹, Zhongqing Wang¹, Huiyuan Li²

1 University of Shanghai for Science and Technology, Shanghai 200093, China;
2 State Key Laboratory of Computer Science/Laboratory of Parallel Computing, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China

Received:2018-05-11 Revised:2018-09-03 Online:2019-06-20 Published:2019-06-20
Contact: Zhongqing Wang, Xuhong Yu, Huiyuan Li E-mail:zqwang@usst.edu.cn;xhyu@usst.edu.cn;huiyuan@iscas.ac.cn
Supported by:
The work is supported by the National Natural Science Foundation of China (Nos. 11571238, 11601332, 91130014, 11471312 and 91430216).

Abstract

Abstract: 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 infnite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the efectiveness and the spectral accuracy.

Key words: Generalized Jacobi polynomials, Spectral method, Jacobi-Sobolev orthogonal basis functions, Elliptic boundary value problems, Error analysis

CLC Number:

Xuhong Yu, Zhongqing Wang, Huiyuan Li. Jacobi-Sobolev Orthogonal Polynomials and Spectral Methods for Elliptic Boundary Value Problems[J]. Communications on Applied Mathematics and Computation, 2019, 1(2): 283-308.

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Jacobi-Sobolev Orthogonal Polynomials and Spectral Methods for Elliptic Boundary Value Problems

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