RBFs for Integral Equations with a Weakly Singular Kernel

Abstract

In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.