Second order Jacobi approximation with applications to fourth-order differential equations

被引：20

作者：

Guo, BY ^{[1
]}

Wang, ZQ

Wan, ZS

Chu, DL

机构：

[1] Shanghai Normal Univ, Dept Math, Div Comp Sci, E Inst, Shanghai 200234, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China

[3] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

APPLIED NUMERICAL MATHEMATICS | 2005年 / 55卷 / 04期

关键词：

second order Jacobi approximation; spectral method for fourth-order problems; convergence; numerical results;

D O I：

10.1016/j.apnum.2005.01.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Second order Jacobi approximation in non-uniformly weighted Sobolev space is investigated. Some approximation results on various orthogonal projections are established, which serve as the mathematical foundation of Jacobi spectral methods for differential equations of fourth order. Jacobi spectral schemes are provided for several model problems. The convergence is proved. Numerical results agree well with theoretical analysis and show the efficiency of this new approach. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：480 / 502

页数：23

共 26 条

[1]

[Anonymous], 1980, TEUBNER TEXTE MATH

[2]

[Anonymous], 1989, CHEBYSHEV FOURIER SP

[3] Direct and inverse approximation theorems for the p-version of the finite element method in the framework of weighted Besov spaces.: Part I:: Approximability of functions in the weighted Besov spaces [J].

Babuska, I ;

Guo, BQ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1512-1538

[4]

Babuska I, 2000, NUMER MATH, V85, P219, DOI 10.1007/s002110000130

[5]

BEDHACHMI Z, 2001, SIAM J NUMER ANAL, V38, P1926

[6] A rational approximation and its applications to differential equations on the half line [J].

Guo B.-Y. ;

Shen J. ;

Wang Z.-Q. .

Journal of Scientific Computing, 2000, 15 (02) :117-147

[7]

Bergh J., 1976, INTERPOLATION SPACES

[8]

BERNARDI C, 1999, SERIES APPL MATH, V3

[9]

Bernardi C, 1997, Handbook of numerical analysis, VV, DOI [10.1016/S1570-8659(97)80003-8, DOI 10.1016/S1570-8659(97)80003-8]

[10]

Canuto C., 2012, Spectral Methods: Fundamentals in Single Domains

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