Utilizing feed-back neural network approach for solving linear Fredholm integral equations system

作     者：Jafarian, A. Nia, S. Measoomy 

作者机构：Islamic Azad Univ Dept Math Urmia Branch Orumiyeh Iran 

出 版 物：《APPLIED MATHEMATICAL MODELLING》 (应用数学模型)

年 卷 期：2013年第37卷第7期

页      面：5027-5038页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：Fredholm integral equation systems Feed-back neural networks (FNN) Cost function Approximate solution Learning algorithm 

摘      要：This paper intended to offer an architecture of artificial neural networks (NNs) for finding approximate solution of a second kind linear Fredholm integral equations system. For this purpose, first we substitute the N-th truncation of the Taylor expansion for unknown functions in the origin system. By applying the suggested neural network for adjusting the real coefficients of given expansions in resulting system. The proposed NN is a two-layer feedback neural network such that it can get a initial vector and then calculates it s corresponding output vector. In continuance, a cost function is defined by using output vector and the target outputs. Consequently, the reported NN using a learning algorithm that based on the gradient descent method, will adjust the coefficients in given Taylor series. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalization and high accuracy. The proposed method is illustrated by several examples with computer simulations. (C) 2012 Elsevier Inc. All rights reserved.