Diagonalized Chebyshev Rational Spectral Methods for Second-Order Elliptic Problems on Unbounded Domains

被引：7

作者：

Ren, Yanmin ^{[1
]}

Yu, Xuhong ^{[1
]}

Wang, Zhongqing ^{[1
]}

机构：

[1] Univ Shanghai Sci & Technol, Sch Sci, Shanghai 200093, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2019年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Chebyshev rational spectral methods; Sobolev bi-orthogonal functions; second-order elliptic equations; numerical results; PARTIAL-DIFFERENTIAL-EQUATIONS; GENERALIZED LAGUERRE FUNCTIONS; GALERKIN METHOD; APPROXIMATION;

D O I：

10.4208/nmtma.OA-2018-0022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Diagonalized Chebyshev rational spectral methods for solving second-order elliptic problems on the half/whole line are proposed. Some Sobolev bi-orthogonal rational basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions can be represented as infinite and truncated Fourier-like Chebyshev rational series. Numerical results demonstrate the effectiveness of the suggested approaches.

引用

页码：265 / 284

页数：20

共 50 条

[21] SUPERCONVERGENT DISCONTINUOUS GALERKIN METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS
Cockburn, Bernardo
Guzman, Johnny
Wang, Haiying
MATHEMATICS OF COMPUTATION, 2009, 78 (265) : 1 - 24
[22] Wavelet methods for second-order elliptic problems, preconditioning, and adaptivity
Lab. d'Analyse Numérique, Universite Pierre et Marie Curie, Tour 55-65, 4 place Jussieu, 75005 Paris, France
Siam J. Sci. Comput., 3 (1006-1026):
[23] CONDITIONS FOR SUPERCONVERGENCE OF HDG METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS
Cockburn, Bernardo
Qiu, Weifeng
Shi, Ke
MATHEMATICS OF COMPUTATION, 2012, 81 (279) : 1327 - 1353
[24] EIGENVALUES OF A SECOND-ORDER ELLIPTIC OPERATOR IN AN UNBOUNDED DOMAIN
HEWGILL, D
PACIFIC JOURNAL OF MATHEMATICS, 1974, 51 (02) : 467 - 476
[25] Solutions of second-order elliptic and parabolic equations of Emden-Fowler type in unbounded domains
Grishina, GV
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2002, 9 (03) : 253 - 274
[26] MULTIGRID METHODS FOR ELLIPTIC PROBLEMS IN UNBOUNDED-DOMAINS
GOLDSTEIN, CI
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1993, 30 (01) : 159 - 183
[27] SUPERCONVERGENT HDG METHODS ON ISOPARAMETRIC ELEMENTS FOR SECOND-ORDER ELLIPTIC PROBLEMS
Cockburn, Bernardo
Qiu, Weifeng
Shi, Ke
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (03) : 1417 - 1432
[28] Mixed methods for nonlinear second-order elliptic problems in three variables
Park, Eun-Jae
Numerical Methods for Partial Differential Equations, 1996, 12 (01):
[29] Domain decomposition algorithms for mixed methods for second-order elliptic problems
Math Comput, 214 (467):
[30] Hermite-Sobolev orthogonal functions and spectral methods for second- and fourth-order problems on unbounded domains
Liu, Yuan
Yu, Xu-hong
Wang, Zhong-qing
Li, Hui-yuan
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (05) : 950 - 970

← 1 2 3 4 5 →