a modified degenerate kernel method

In this paper, the system of Fredholm integral equations of the second kind is investigated by using a modified degenerate kernel  method (MDKM). To construct a MDKM the source function is approximated by the same way of producing degenerate kernel. The interpolation is used to make the needed approximations. Lagrange polynomials are adopted for the interpolation. The equivalency of  proposed method and  Lagrange-collocation method is shown. The error and convergence of the algorithm are given strictly. The efficiency of the approach will be shown by applying the procedure on some prototype examples.