Superconvergence results for the nonlinear Fredholm–Hemmerstein integral equations of second kind

The multi-projection methods for solving the Fredholm-Hammerstein integral equation is proposed in this paper. We obtain the similar super-convergence results as in Mandal and Nelakanti (J Comput Appl Math 319:423–439, 2017) with a smooth kernel using piecewise polynomials of degree $$\le r-1,$$ i.e., for both the multi-Galerkin and multi-collocation methods have order of convergence $$\mathcal O (h^{3r})$$ in uniform norm, where h is the norm of the partition. We have also considered iterated version of these methods and prove that both iterated multi-Galerkin and iterated multi-collocation methods have order of convergence $$\mathcal O(h^{4r})$$ in uniform norm. Numerical examples are given to illustrate the theoretical results.