The method of radial basis functions for the solution of nonlinear Fredholm integral equations system

In this paper, an eective simple method is proposed for approximating the solution of Fredholm integral equations systems using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadrat- ics (MQs), using Legendre-Gauss-Lobatto nodes and weights. A theorem is presented to prove the convergence of the algorithm as well. Some numerical examples are illustrated and the results compared with those obtained by triangular functions (TFs), delta basis functions (DFs), block-pulse functions (BPFs), Sinc fucntion, Adomian decomposition, Haar wavelet and direct methods demonstrate the validity, accuracy and applicability of the RBF method.