Title: Feedback neural network method for solving linear Volterra integral equations of the second kind

Authors: Ahmad Jafarian; Safa Measoomy Nia

Addresses: Department of Mathematics, Islamic Azad University, Urmia Branch, P.O. Box: 57196-96157, Urmia, Iran ' Department of Mathematics, Islamic Azad University, Urmia Branch, P.O. Box: 57196-96157, Urmia, Iran

Abstract: Integral equations play major roles in different fields of science and engineering, therefore, a new method for finding a solution of the Volterra integral equation is presented. So we have applied a structure of hybrid neural networks (NNs). The proposed neural net can get a real input vector and calculates its corresponding output vector. Next, a learning algorithm based on the gradient descent method has been defined for adjusting the connection weights. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalisation and high accuracy. The proposed method is illustrated by several examples with computer simulations.

Keywords: Volterra integral equations; hybrid neural nets; feedback neural networks; FNN; cost function; simulation.

DOI: 10.1504/IJMMNO.2013.056531

International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.3, pp.225 - 237

Received: 19 Jan 2013
Accepted: 01 May 2013

Published online: 25 Sep 2013 *

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