The main purpose of this investigation is to obtain a computational method for solving nonlinear logarithmic singular Volterra integral equations of the second kind. The method is based on the use of shape functions of the moving least squares approximation constructed on scattered points in the discrete Galerkin method. To compute singular integrals appearing in the process of the scheme, we apply a particular nonuniform integration rule. The algorithm of the presented scheme is attractive and easy to implement on computers. The proposed scheme does not require any background meshes, so it is meshless. Finally, a numerical example is presented to illustrate the efficiency and accuracy of the new technique.
