Solving Nonlinear Differential Equations by a Neural Network Method

Authors:
Lucie P. Aarts;Peter Van der Veer
Affiliations:
-;-
Venue:
ICCS '01 Proceedings of the International Conference on Computational Science-Part II
Year:
2001

Citing 5
Cited 0

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Abstract

In this paper we demonstrate a neural network method to solve nonlinear differential equations and its boundary conditions. The idea of our method is to incorporate knowledge about the differential equation and its boundary conditions into neural networks and the training sets. Hereby we obtain specifically structured neural networks. To solve the nonlinear differential equation and its boundary conditions we have to train all obtained neural networks simultaneously. This is realized by applying an evolutionary algorithm.