A numerical method to solve a Fredholm integral equation of the second kind is studied. This approach is based on a collocation method and Sloan iterations. Our solution is represented by a linear combination of minimal splines, and the coe cients are calculated by a method of local approximation (quasi-interpolation). The results of numerical experiments demonstrating how the quality of approximation can be improved by using minimal trigonometric splines and corresponding functionals in comparison with several earlier suggested approaches are presented.