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dc.contributor.author | Arnau i Córdoba, Josep Vicent![]() |
es_ES |
dc.contributor.author | Fullana Alfonso, Màrius Josep![]() |
es_ES |
dc.date.accessioned | 2023-02-28T19:00:54Z | |
dc.date.available | 2023-02-28T19:00:54Z | |
dc.date.issued | 2022-02 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/192166 | |
dc.description.abstract | [EN] In this work, we present some techniques applicable to Initial Value Problems when solving a System of Ordinary Differential Equations (ODE). Such techniques should be used when applying adaptive step-size numerical methods. In our case, a Runge-Kutta-Fehlberg algorithm (RKF45) has been employed, but the procedure presented here can also be applied to other adaptive methods, such as N-body problems, as AP3M or similar ones. By doing so, catastrophic cancellations were eliminated. A mathematical optimization was carried out by introducing the objective function in the ODE System (ODES). Resizing of local errors was also utilised in order to adress the problem. This resize implies the use of certain variables to adjust the integration step while the other variables are used as parameters to determine the coefficients of the ODE system. This resize was executed by using the asymptotic solution of this system. The change of variables is necessary to guarantee the stability of the integration. Therefore, the linearization of the ODES is possible and can be used as a powerful control test. All these tools are applied to a physical problem. The example we present here is the effective numerical resolution of Lemaitre-Tolman-Bondi space-time solutions of Einstein Equations. | es_ES |
dc.description.sponsorship | This research was patially funded by the Spanish Ministerio de Ciencia, Innovación y Universidades and the Fondo Europeo de Desarrollo Regional, Projects PID2019-109753GB-C21 and PID2019-109753GB-C22, the Generalitat Valenciana Project AICO/2020/125 and the Universitat de València Special Action Project UV-INVAE19-1197312. The APC was funded by the Spanish Ministerio de Ciencia, Innovación y Universidades and the Fondo Europeo de Desarrollo Regional, Projects PID2019-109753GB-C21 and PID2019-109753GB-C22. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | MDPI AG | es_ES |
dc.relation.ispartof | Mathematics | es_ES |
dc.rights | Reconocimiento (by) | es_ES |
dc.subject | Numerical | es_ES |
dc.subject | Initial value problem | es_ES |
dc.subject | Ordinary differential equations systems | es_ES |
dc.subject | Exact solutions of einstein equations | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Resolution of Initial Value Problems of Ordinary Differential Equations Systems | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.3390/math10040593 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-109753GB-C21/ES/POSICIONAMIENTO RELATIVISTA Y ECUACIONES DE EINSTEIN/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/GVA//AICO%2F2020%2F125/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-109753GB-C22/ES/TEORIA DE CAMPOS Y GRAVITACION/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/UV//UV-INVAE19-1197312//Special Action Project/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Gestión en la Edificación - Escola Tècnica Superior de Gestió en l'Edificació | es_ES |
dc.description.bibliographicCitation | Arnau I Córdoba, JV.; Fullana Alfonso, MJ. (2022). Resolution of Initial Value Problems of Ordinary Differential Equations Systems. Mathematics. 10(4):1-27. https://doi.org/10.3390/math10040593 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.3390/math10040593 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 27 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 10 | es_ES |
dc.description.issue | 4 | es_ES |
dc.identifier.eissn | 2227-7390 | es_ES |
dc.relation.pasarela | S\455936 | es_ES |
dc.contributor.funder | Generalitat Valenciana | es_ES |
dc.contributor.funder | Universitat de València | es_ES |
dc.contributor.funder | AGENCIA ESTATAL DE INVESTIGACION | es_ES |
dc.contributor.funder | Agencia Estatal de Investigación | es_ES |
dc.contributor.funder | European Regional Development Fund | es_ES |
upv.costeAPC | 1400 | es_ES |