Validated solutions of initial value problems for ordinary differential equations

被引：236
作者：
Nedialkov, NS [1 ]
Jackson, KR
Corliss, GF
机构：
[1] Univ Toronto, Dept Comp Sci, Toronto, ON M5S 3G4, Canada
[2] Marquette Univ, Dept Math Stat & Comp Sci, Milwaukee, WI 53201 USA
来源：
APPLIED MATHEMATICS AND COMPUTATION | 1999年 / 105卷 / 01期
关键词：
initial value problems; ordinary differential equations; interval arithmetic; Taylor series methods;
D O I：
10.1016/S0096-3003(98)10083-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Compared to standard numerical methods for initial-value problems (IVPs) for ordinary differential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated solutions of IVPs for ODEs, describe several such methods in a common framework, and identify areas for future research. (C) 1999 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：21 / 68
页数：48
相关论文
共 43 条
[21]   INTERVAL ARITHMETIC ERROR-BOUNDING ALGORITHMS [J].
JACKSON, LW .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (02) :223-238
[22]  
KERBL M, 1991, IMACS ANN COMPUTING, V12
[23]  
KRUCKEBERG F, 1969, TOPICS INTERVAL ANAL, P91
[24]  
Kulisch U, 1981, COMPUTER ARITHMETIC, DOI DOI 10.1016/C2013-0-11018-5
[25]  
LOHNER R. J., 1987, WILEY TEUBNER SERIES, P255
[26]  
LOHNER RJ, 1995, SCICADE 95 INT C SCI
[27]  
LOHNER RJ, 1978, THESIS U KARLSRUHE
[28]  
Moore R. E., 1984, Proceedings of the 23rd IEEE Conference on Decision and Control (Cat. No. 84CH2093-3), P1529
[29]  
Moore R. E., 1965, ERROR DIGITAL COMPUT, V1, P61
[30]  
Moore R.E., 1965, ERROR DIGIT COMPUT, V2, P103
12345