Artificial neural networks for solving ordinary and partial differential equations
| dc.contributor.author | Lagaris, I. E. | en |
| dc.contributor.author | Likas, A. | en |
| dc.contributor.author | Fotiadis, D. I. | en |
| dc.date.accessioned | 2015-11-24T17:03:00Z | |
| dc.date.available | 2015-11-24T17:03:00Z | |
| dc.identifier.issn | 1045-9227 | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/11120 | |
| dc.rights | Default Licence | - |
| dc.subject | collocation method | en |
| dc.subject | finite elements | en |
| dc.subject | neural networks | en |
| dc.subject | neuroprocessors | en |
| dc.subject | ordinary differential equations | en |
| dc.subject | partial differential equations | en |
| dc.title | Artificial neural networks for solving ordinary and partial differential equations | en |
| heal.abstract | We 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.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.journalName | Ieee Transactions on Neural Networks | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 1998 | - |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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