In this study, we address the problem of locating and approximating solutions of nonlinear Hammerstein-type integral equations with non-separable kernels by employing a higher-order iterative method. To facilitate this process, in the first place, we approximate the non-separable kernel by a separable one and to continue we modify the fifth order iterative method in Arroyo et al. Approximation of artificial satellites' preliminary orbits: the efficiency challenge. Mathematical and Computer Modelling. 2011;54(7–8):1802–1807 by approximating a solution of a nonlinear Hammerstein-type integral equation. Next, we establish the convergence analysis of a fifth order iterative method, particularly focused on restricted global convergence. After that, we presented the theoretical domains of existence and uniqueness of the solution, by which we are able to find the best ball of location, separation, and uniqueness. Moreover, we examine the effectiveness of approximation of the inverse operator, especially as the number of terms increases in the separable kernel and outline the procedure used to construct the respective operator. We consider a nonlinear Hammerstein-type integral equation to validate the theoretical results.
Dua et al. (Fri,) studied this question.