Projection and modified projection methods for nonlinear Hammerstein integral equations on the real line using Hermite polynomials

Many physical problems represented as initial and boundary value problems are usually solved by transforming them into integral equations on the real line. Therefore, this paper proposes polynomially based projection and modified projection methods to solve Hammerstein integral equations on the real line with sufficiently smooth kernels. The approximating operator employed is either the orthogonal projection or an interpolatory projection using Hermite polynomials as basis functions. We analyse the convergence of the proposed approaches and its iterated version and we establish superconvergence results. Through different numerical tests, the effectiveness of the proposed methods is presented to demonstrate the given theoretical framework.