Error estimation of Hermite spectral method for nonlinear partial differential equations

被引：145

作者：

Guo, BY ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 201800, Peoples R China

来源：

MATHEMATICS OF COMPUTATION | 1999年 / 68卷 / 227期

关键词：

Hermite approximation; Burgers equation; error estimations;

D O I：

10.1090/S0025-5718-99-01059-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Hermite approximation is investigated. Some inverse inequalities, imbedding inequalities and approximation results are obtained. A Hermite spectral scheme is constructed for Burgers equation. The stability and convergence of the proposed scheme are proved strictly. The techniques used in this paper are also applicable to other nonlinear problems in unbounded domains.

引用

页码：1067 / 1078

页数：12

共 18 条

[1]

Adams A, 2003, SOBOLEV SPACES

[2]

BLACK K, UNPUB SPECTRAL ELEME

[3] SPECTRAL METHODS USING RATIONAL BASIS FUNCTIONS ON AN INFINITE INTERVAL [J].

BOYD, JP .

JOURNAL OF COMPUTATIONAL PHYSICS, 1987, 69 (01) :112-142

[4] A COMPLETE ORTHONORMAL SYSTEM OF FUNCTIONS IN L2(-INFINITY, INFINITY) SPACE [J].

CHRISTOV, CI .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1982, 42 (06) :1337-1344

[5] LAGUERRE SPECTRAL APPROXIMATION OF ELLIPTIC PROBLEMS IN EXTERIOR DOMAINS [J].

COULAUD, O ;

FUNARO, D ;

KAVIAN, O .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1990, 80 (1-3) :451-458

[6] Partial differential equations of mathematical physics [J].

Courant, R ;

Friedrichs, K ;

Lewy, H .

MATHEMATISCHE ANNALEN, 1928, 100 :32-74

[7]

Funaro D., 1991, ORTHOGONAL POLYNOMIA, V9, P263

[8]

FUNARO D, 1990, MATH COMPUT, V57, P597

[9]

Guo B., 1974, Acta Math. Sin, V17, P242

[10]

Guo B.Y., 1994, CONT MATH, V163, P33

← 1 2 →