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Please use this identifier to cite or link to this item: https://olympias.lib.uoi.gr/jspui/handle/123456789/11120
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dc.contributor.authorLagaris, I. E.en
dc.contributor.authorLikas, A.en
dc.contributor.authorFotiadis, D. I.en
dc.date.accessioned2015-11-24T17:03:00Z-
dc.date.available2015-11-24T17:03:00Z-
dc.identifier.issn1045-9227-
dc.identifier.urihttps://olympias.lib.uoi.gr/jspui/handle/123456789/11120-
dc.rightsDefault Licence-
dc.subjectcollocation methoden
dc.subjectfinite elementsen
dc.subjectneural networksen
dc.subjectneuroprocessorsen
dc.subjectordinary differential equationsen
dc.subjectpartial differential equationsen
dc.titleArtificial neural networks for solving ordinary and partial differential equationsen
heal.typejournalArticle-
heal.type.enJournal articleen
heal.type.elΆρθρο Περιοδικούel
heal.languageen-
heal.accesscampus-
heal.recordProviderΠανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικήςel
heal.publicationDate1998-
heal.abstractWe present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial/boundary conditions. This part involves a feedforward neural net work containing adjustable parameters (the weights). Hence by construction the initial/boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ordinary differential equations (ODE's), to systems of coupled ODE's and also to partial differential equations (PDE's). In this article, we illustrate the method by solving a variety of model problems and present comparisons with solutions obtained using the Galekrkin finite element method for several cases of partial differential equations. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.en
heal.journalNameIeee Transactions on Neural Networksen
heal.journalTypepeer reviewed-
heal.fullTextAvailabilityTRUE-
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