Superconvergent Nyström and degenerate kernel methods for Hammerstein integral equations

In a recent paper, we introduced new methods called superconvergent Nyström and degenerate kernel methods for approximating the solution of Fredholm integral equations of the second kind with a smooth kernel. In this paper, these methods are applied to numerically solve the Hammerstein equations. By using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomials of degree ≤r−1≤r−1, we prove that, as for Fredholm integral equations, the proposed methods exhibit convergence orders 3r3r and 4r4r for the iterated version. Several numerical examples are given to demonstrate the effectiveness of the current methods.