Solving differential equations with constructed neural networks

Authors:
Ioannis G. Tsoulos;Dimitris Gavrilis;Euripidis Glavas
Affiliations:
Department of Communications, Informatics and Management, Technological Educational Institute of Epirus, Greece;Digital Curation Unit Athena Research Centre, Artemidos 6 & Epidavrou, 15125 Maroussi, Greece;Department of Communications, Informatics and Management, Technological Educational Institute of Epirus, Greece
Venue:
Neurocomputing
Year:
2009

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Abstract

A novel hybrid method for the solution of ordinary and partial differential equations is presented here. The method creates trial solutions in neural network form using a scheme based on grammatical evolution. The trial solutions are enhanced periodically using a local optimization procedure. The proposed method is tested on a series of ordinary differential equations, systems of ordinary differential equations as well as on partial differential equations with Dirichlet boundary conditions and the results are reported.