Solving Hammerstein-Type Integral Equations with Polynomial Nemystkii Operator

Abstract In this study, we use a family of third-order iterative methods to locate, separate, and approximate a solution of non-linear integral equations of Hammerstein type. We will consider two situations, when the kernel of the integral equation is separable and when it is not separable. When the kernel is non-separable, we will approximate the given integral equation by means of a new one with a separable kernel, and this transformation allows us to locate and approximate a solution of the first integral equation. To apply our theoretical findings, various examples have been tested.