Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 35-43 |
| Number of pages | 9 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 52 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Jul 20 1994 |
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Keywords
- Chaos
- Numerical orbits
- Ordinary differential equations
- Shadowing
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
Cite this
Shadowing orbits of ordinary differential equations. / Coomes, Brian A; Kocak, Huseyin; Palmer, Kenneth J.
In: Journal of Computational and Applied Mathematics, Vol. 52, No. 1-3, 20.07.1994, p. 35-43.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Shadowing orbits of ordinary differential equations
AU - Coomes, Brian A
AU - Kocak, Huseyin
AU - Palmer, Kenneth J.
PY - 1994/7/20
Y1 - 1994/7/20
N2 - 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.
AB - 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.
KW - Chaos
KW - Numerical orbits
KW - Ordinary differential equations
KW - Shadowing
UR - http://www.scopus.com/inward/record.url?scp=0028479087&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0028479087&partnerID=8YFLogxK
U2 - 10.1016/0377-0427(94)90347-6
DO - 10.1016/0377-0427(94)90347-6
M3 - Article
AN - SCOPUS:0028479087
VL - 52
SP - 35
EP - 43
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1-3
ER -