Validated solutions of initial value problems for ordinary differential equations

被引：232

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

页码：21 / 68

页数：48

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