Publication
Effective computability of solutions of differential inclusions-the ten thousand monkeys approach
| dc.contributor.author | Collins, Pieter | |
| dc.contributor.author | Graça, Daniel | |
| dc.date.accessioned | 2012-04-13T08:43:10Z | |
| dc.date.available | 2012-04-13T08:43:10Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | In this note we consider the computability of the solution of the initial- value problem for ordinary di erential equations with continuous right- hand side. We present algorithms for the computation of the solution using the \thousand monkeys" approach, in which we generate all possi- ble solution tubes, and then check which are valid. In this way, we show that the solution of a di erential equation de ned by a locally Lipschitz function is computable even if the function is not e ectively locally Lips- chitz. We also recover a result of Ruohonen, in which it is shown that if the solution is unique, then it is computable, even if the right-hand side is not locally Lipschitz. We also prove that the maximal interval of existence for the solution must be e ectively enumerable open, and give an example of a computable locally Lipschitz function which is not e ectively locally Lipschitz. | por |
| dc.identifier.other | AUT: DGR01772; | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/1017 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.relation.publisherversion | http://www.jucs.org/jucs_15_6/effective_computability_of_solutions | por |
| dc.subject | Ordinary differential equations | por |
| dc.subject | Lipschitz condition | por |
| dc.subject | Differential inclusions | por |
| dc.subject | Semicomputability | por |
| dc.subject | Computable analysis | por |
| dc.title | Effective computability of solutions of differential inclusions-the ten thousand monkeys approach | por |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/SFRH/SFRH%2FBPD%2F39779%2F2007/PT | |
| oaire.citation.endPage | 1185 | por |
| oaire.citation.issue | 15 | por |
| oaire.citation.startPage | 1162 | por |
| oaire.citation.title | Journal of Universal Computer Science | 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 | article | por |
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