Constructive analysis of periodic solutions with interval halving: Doc 319

For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both study the solvability and construct approximations to the solution. An interval halving te...

Full description

Saved in:
Bibliographic Details
Published in:Boundary value problems 2013-03, Vol.2013, p.1
Main Authors: Rontó, András, Rontó, Miklós, Shchobak, Nataliya
Format: Article
Language:English
Subjects:
Boundary value problems
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both study the solvability and construct approximations to the solution. An interval halving technique, by using which one can weaken significantly the conditions required to guarantee the convergence, is introduced. The main assumption on the equation is that the non-linearity is locally Lipschitzian. An existence theorem based on properties of approximations is proved. A relation to Mawhin's continuation theorem is indicated. MSC: 34B15.[PUBLICATION ABSTRACT]
ISSN:1687-2762
1687-2770
DOI:10.1186/1687-2770-2013-57