An iterative algorithm to find a closed form of solution for Hammerstein nonlinear integral equation constructed by the concept of cosm‑rs

In this article, we study Hammerstein nonlinear integral equation introduced by the concept of conductor-like screening model for real solvent. We use a combination of modified homotopy perturbation and Adomian decomposition method to solve the above nonlinear integral equation. The approach is based on preparing a closed form of solution to recognize the Hammerstein integral equation for the determination of the chemical potential of a surface segment as a function of screening charge density. This solution can be more effective in analyzing the future concept on the above chemical problem and decrease computational operations. Finally, we prove convergence of the proposed method and compare our results to some other works to show validity and high accuracy.