Legendre superconvergent degenerate kernel and Nyström methods for nonlinear integral equations - Allouch, C.; Arrai, M.; Bouda, H.; Tahrichi, M. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.9We study polynomially based superconvergent collocation methods for the approximation of solutions of nonlinear integral equations. The superconvergent degenerate kernel method is chosen for approximating the solutions of Hammerstein equations, while a superconvergent Nystr\"om method is used for solving Urysohn equations. By applying interpolatory projections based on Legendre polynomials of degree $≤ n,$ we analyze the superconvergence of these methods and their iterated versions. Numerical results are presented to validate the theoretical results.