Universal approximation method for the solution of integral equations

Universal approximation method for the solution of integral equations In this paper, we present a novel approach for approximating Hammerstein–Volterra delay integral equations (HVDIEs) by applying the universal approximation method through an artificial intelligence utility in a simple way. In this paper, neural network model (NNM) is applied as universal approximators for any nonlinear continuous functions. Here, neural network is considered as a part of large field called neural computing or soft computing. With this capability, the solution of Hammerstein–Volterra delay integral equation can be approximated by the appropriate NNM within an arbitrary accuracy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Sciences Springer Journals

Universal approximation method for the solution of integral equations

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Applications of Mathematics
ISSN
2008-1359
eISSN
2251-7456
D.O.I.
10.1007/s40096-017-0212-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we present a novel approach for approximating Hammerstein–Volterra delay integral equations (HVDIEs) by applying the universal approximation method through an artificial intelligence utility in a simple way. In this paper, neural network model (NNM) is applied as universal approximators for any nonlinear continuous functions. Here, neural network is considered as a part of large field called neural computing or soft computing. With this capability, the solution of Hammerstein–Volterra delay integral equation can be approximated by the appropriate NNM within an arbitrary accuracy.

Journal

Mathematical SciencesSpringer Journals

Published: Feb 16, 2017

References

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