A STABILITY RESULT FOR SECTORIAL OPERATORS IN BANACH-SPACES

被引：64
作者：
PALENCIA, C
机构：
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 1993年 / 30卷 / 05期
关键词：
HOLOMORPHIC SEMIGROUPS; PARABOLIC PROBLEMS; STABILITY; BANACH SPACES; MAXIMUM NORM; A-ACCEPTABLE RATIONAL METHODS; CRANK-NICOLSON SCHEME;
D O I：
10.1137/0730071
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper the author considers approximations of holomorphic semigroups on general Banach spaces based on A-acceptable rational functions. A general stability theorem is proved. It covers rational functions r(z) with \r(infinity)\ = 1 and can be applied even to variable step cases. In particular the question of the L(p)-stability (p not-equal 2) of Crank-Nicolson schemes for parabolic initial value problems is settled.
引用
收藏
页码：1373 / 1384
页数：12
相关论文
共 26 条
[1]  
Bonsall F. F., 1971, LONDON MATH SOC LECT, V2
[2]   RATIONAL APPROXIMATIONS OF SEMIGROUPS [J].
BRENNER, P ;
THOMEE, V .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (04) :683-694
[3]  
BRENNER P, 1975, LECTURE NOTES MATH, V434
[4]  
CLEMENT P, 1987, 1 PARAMETER SEMIGROU
[5]  
CROUZIEX M, IN PRESS BIT
[6]  
Dekker K., 1984, STABILITY RUNGE KUTT
[7]  
Dunford N, 1958, LINEAR OPERATORS, VI
[8]  
Foias C., 1970, HARMONIC ANAL OPERAT
[9]   HIGH-ACCURACY STABLE DIFFERENCE SCHEMES FOR WELL-POSED INITIAL-VALUE PROBLEMS [J].
HERSH, R ;
KATO, T .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (04) :670-682
[10]  
Hille E., 1957, FUNCTIONAL ANAL SEMI
123