Radial basis function networks in the numerical solution of linear integro-differential equations

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.