Numerical solution of the second kind integral equations using radial basis function networks

In this paper, a new method using radial basis function (RBF) networks is presented for solving the linear second kind integral equations of Fredholm and Volterra types. This method employs a growing neural network as the approximate solution of the integral equations, whose the activation functions are RBFs. The parameters (weights, centers and widths) of the approximate solution are adjusted by using an unconstrained optimization problem. Numerical results show that our method has the potentiality to become an efficient approach for solving integral equations.