Neural network application to solve Fredholm integral equations of the second kind

Abstract

In this paper, a novel method based on neural networks is presented for solving Fredholm<br><br>integral equations of the second kind. In the present approach, we first approximate the<br><br>unknown function based on neural network, then substitute the approximate function in the<br><br>appropriate error function of the integral equation, and finally train the network with as few<br><br>neurons as necessary to achieve the desired accuracy. This novel method, in comparison with<br><br>existing numerical methods shows that the use of neural networks provides solutions with<br><br>very good generalizations and higher accurac.