Numerical solution of nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel by spline quasi-interpolating projectors

Nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel are here taken into account and numerically solved by spline quasi-interpolating projectors based collocation and Kulkarni methods, both in their basic and iterated versions. Theoretical analysis of discretization error and convergence order is provided, together with numerical results validating the estimates obtained under the hypothesis of sufficiently smooth solutions. Finally, some results in case of less regular solutions show the robustness of the proposed approach even in a non smooth framework.