Search

Abstract: The purpose of this paper is to present a new method to solve the linear integro-differential equations using radial basis function (RBF) networks. The approximate solution is represented by means of RBFs, whose coefficients are computed by training a RBF network, and is written as a sum of two parts. The first part employs a growing RBF network, whose parameters are adjusted to minimize an appropriate error function, and are constructed so as not to effect the supplementary conditions of the equations. The second part only satisfies the supplementary conditions. Numerical examples are given to demonstrate the proposed idea and method. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a new method based on radial basis functions (RBFs) and iterative procedure for the solution of linear integral equations of Fredholm and Volterra types of the second kind. To obtain a primary approximate solution, the collocation method with a small number of nodes, based on the RBFs and their first-order derivatives, can be adapted. Moreover, we present an iterative procedure from the integral equation to improve the accuracy of solution. Numerical examples show that our approach has the potentiality to become an efficient method. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]