Publication
The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable
| dc.contributor.author | Graça, Daniel | |
| dc.contributor.author | Zhong, Ning | |
| dc.contributor.author | Buescu, Jorge | |
| dc.date.accessioned | 2012-04-13T08:05:54Z | |
| dc.date.available | 2012-04-13T08:05:54Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | Let (®, ¯) ½ R denote the maximal interval of existence of solution for the initial-value problem ½ dx dt = f(t, x), f : E ! Rm,E is an open subset of Rm+1 x(t0) = x0, with (t0, x0) 2 E. We show that (®, ¯) is r.e. (recursively enumerable) open and the solution x(t) defined on (®, ¯) is computable, provided that (a) f is computable and effectively locally Lipschitz, and (b) (t0, x0) is a computable point. We also prove that this result is the best in the sense that, for some initial-value problems satisfying (a) and (b), their maximal intervals of existence are non-recursive. | por |
| dc.identifier.other | AUT: DGR01772; | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/1006 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.publisher | G.Hanrot and P.Zimmermann | por |
| dc.title | The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable | por |
| dc.type | conference object | |
| dspace.entity.type | Publication | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/SFRH/SFRH%2FBD%2F17436%2F2004/PT | |
| oaire.citation.endPage | 40 | por |
| oaire.citation.startPage | 33 | por |
| oaire.citation.title | Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7) | por |
| oaire.fundingStream | SFRH | |
| person.familyName | Graça | |
| person.givenName | Daniel | |
| person.identifier.ciencia-id | 2D11-56DE-3F11 | |
| person.identifier.orcid | 0000-0002-0330-833X | |
| person.identifier.rid | D-2335-2011 | |
| person.identifier.scopus-author-id | 8882791800 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | por |
| rcaap.type | conferenceObject | por |
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