New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations

This research aims to propose a new family of one-parameter multi-step iterative methods that combine the homotopy perturbation method with quadrature formula for solving nonlinear equations. The proposed are based on higher-order convergence scheme allows faster and more efficient compared existing methods. It also demonstrate efficiency index can reach up 43≈1.587 84≈1.681, respectively, indicating high degree accuracy in To evaluate effectiveness suggested methods, several numerical examples including their performance provided