This paper explores recent advancements in enhancing the stability of iterative methods, focusing specifically on higher-order modifications of Steffensen's method for solving systems of non-linear equations. Steffensen's method is a popular choice for its simplicity and efficiency; however, its convergence behavior can be sensitive to certain problem characteristics. Recent developments have aimed at improving the stability and robustness of Steffensen's method by incorporating higher-order modifications and adaptive strategies. Through theoretical analysis and empirical evaluations, this paper reviews these recent developments, discusses their implications for solving non-linear equation systems, and identifies future research directions.

Keywords: Steffensen's Method, Higher-Order Modification, Non-Linear Equations, Iterative Techniques, Convergence Rate, Computational Efficiency.