A numerical method based on generalized log orthogonal functions for solving cordial Volterra integral equations of the third kind

‎This paper is devoted to solving cordial Volterra integral equations of the third kind‎. First, ‎generalized log orthogonal functions are introduced and their properties is investigated. ‎Then by using this kind of orthogonal functions as basis function in spectral collocation method, a numerical method is proposed to solve this kind of integral equations. ‎ ‎The approximation error and convergence analysis of the presented method are investigated‎. In order to verify the efficiency and accuracy of the presented method ‎‎ ‎several numerical examples have been considered‎. ‎A comparison of the obtained results demonstrates that the current method is less expensive and more efficient than some previously proposed methods‎.