The main purpose of this paper is to describe a method for the numerical solution of Volterra integral equations of the second kind with logarithmic kernels utilizing radial basis functions (RBFs). The scheme is based on the junction of the product integration method and the collocation method. Since the presented method does not require any background mesh for its approximation and numerical integration, it is called the meshless product integration (MPI) method. The method is effective and its algorithm can be easily implemented. The validity and efficiency of the new technique are demonstrated through a numerical example.
