SHADOWING ORBITS OF ORDINARY DIFFERENTIAL-EQUATIONS

被引：17

作者：

COOMES, BA ^{[1
]}

KOCAK, H ^{[1
]}

PALMER, KJ ^{[1
]}

机构：

[1] UNIV MIAMI,DEPT MATH & COMP SCI,CORAL GABLES,FL 33124

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1994年 / 52卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

NUMERICAL ORBITS; ORDINARY DIFFERENTIAL EQUATIONS; SHADOWING; CHAOS;

D O I：

10.1016/0377-0427(94)90347-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new notion of shadowing of a pseudo orbit, an approximate solution, of an autonomous system of ordinary differential equations by an associated nearby true orbit is introduced. Then a general shadowing theorem for finite time, which guarantees the existence of shadowing in ordinary differential equations and provides error bounds for the distance between the true and the pseudo orbit in terms of computable quantities, is proved. The use of this theorem in numerical computations of orbits is outlined.

引用

页码：35 / 43

页数：9

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