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

[41] Existence and the asymptotic behavior of generalized solutions of the Neumann problem for second-order elliptic equations in unbounded layer domains
Gasymov, MG
Aslanov, GI
DIFFERENTIAL EQUATIONS, 2001, 37 (12) : 1699 - 1710
[42] Lp-theory for second-order elliptic operators with unbounded coefficients
Motohiro Sobajima
Journal of Evolution Equations, 2012, 12 : 957 - 971
[43] Existence and the Asymptotic Behavior of Generalized Solutions of the Neumann Problem for Second-Order Elliptic Equations in Unbounded Layer Domains
M. G. Gasymov
G. I. Aslanov
Differential Equations, 2001, 37 : 1699 - 1710
[44] L p -theory for second-order elliptic operators with unbounded coefficients
Sobajima, Motohiro
JOURNAL OF EVOLUTION EQUATIONS, 2012, 12 (04) : 957 - 971
[45] RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS
Tang, Tao
Wang, Li-Lian
Yuan, Huifang
Zhou, Tao
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (02): : A585 - A611
[46] Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains
Hideo Kozono
Yutaka Terasawa
Yuta Wakasugi
Mathematische Annalen, 2021, 380 : 1105 - 1117
[47] On Some Elliptic Problems in Unbounded Domains
Chipot, Michel
CHINESE ANNALS OF MATHEMATICS SERIES B, 2018, 39 (03) : 597 - 606
[48] Semilinear elliptic problems on unbounded domains
Shindler, I
Tintarev, K
CALCULUS OF VARIATIONS AND DIFFERENTIAL EQUATIONS, 2000, 410 : 210 - 217
[49] On Some Elliptic Problems in Unbounded Domains
Michel CHIPOT
Chinese Annals of Mathematics,Series B, 2018, (03) : 597 - 606
[50] ELLIPTIC PROBLEMS ON UNBOUNDED-DOMAINS
JANSSEN, R
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1986, 17 (06) : 1370 - 1389

← 1 2 3 4 5 →