A neural network approach for solving Fredholm integral equations of the second kind
A neural network approach for solving Fredholm integral equations of the second kind
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DOI：
10.1007/s00521-010-0489-y
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发表时间：
2012-07-01
影响因子：
6
通讯作者：
Buzhabadi, Reza
中科院分区：
文献类型：
--
作者：
Effati, Sohrab;Buzhabadi, Reza
本文提出了一种基于前馈神经网络的解决第二类Fredholm积分方程的新方法。在本方法中，我们首先基于神经网络近似未知函数，然后将近似函数代入积分方程的适当误差函数中，最后用尽可能少的神经元训练网络以达到期望的精度。与 Harr 函数和 Bernstein 多项式方法相比，这种新颖的方法表明，神经网络的使用提供了具有非常好的泛化性和更高的精度的解决方案。通过几个例子说明了所提出的方法。
In this paper, a novel method based on feed-forward neural networks is presented for solving Fredholm integral equations of the second kind. In the present approach, we first approximate the unknown function based on neural networks, then substitute the approximate function in the appropriate error function of the integral equation, and finally train the network with as few neurons as necessary to achieve the desired accuracy. This novel method, in comparison with Harr function and Bernstein polynomials methods, shows that the use of neural networks provides solutions with very good generalizations and higher accuracy. The proposed method is illustrated by several examples.