Spectral Projection Methods for Derivative Dependent Hammerstein Equations with Green’s Kernels

This article proposes projection methods using polynomials for solving nonlinear Hammerstein equations with first derivative dependency and with a Green’s function type kernel. We analyze the convergence analysis of Galerkin and collocation methods with their iterated versions and show that the order of convergence in the iterated projection method improves over the projection method. Orthogonal projection operators and interpolatory projections using Legendre polynomial are both employed. Several numerical experiments demonstrate the efficacy of the suggested methods.