Approximate positive solutions of nonlinear differential equations using neural networks and localization results


Ioana DărăbanAndrei Horvat-Marc


Full PDF

carpathian_2008_24_3_317_326

We present a new method to solve nonlinear differential equations using neural networks. In order to train a neural network, we adjust the data according to a localization result of positive solutions of nonlinear integral equations. The main tool used in the proofs of localization results is a fixed point theorem in a cone, due to Krasnoselskii. Two numerical examples are described to demonstrate the method.

Additional Information

Author(s)

Dărăban, Ioana, Horvat-Marc, Andrei