This article investigates a numerical scheme based on radial basis functions (RBFs) for solving weakly singular integral equations by combining the product integration method and the collocation method. The RBF methodology is an effective technique for the approximation of an unknown function by using a set of scattered points. Since the proposed scheme does not require any background mesh for its approximation and numerical in- tegration unlike other product integration methods, it is called the meshless product integration (MPI) method. The proposed scheme is simple and computationally attractive. This approach reduces the solution of the weakly singular integral equation to the solution of a linear system of algebraic equations. The error analysis of the method is provided. The validity and efficiency of the new technique are demonstrated through several tests.
