In the realm of numerical analysis, solving systems of non-linear equations holds great importance due to its applications in various scientific and engineering domains. Steffensen's method is a well-known iterative technique used to find approximate solutions to such systems. This article proposes a higher-order modification of Steffensen's method to enhance its convergence rate and computational efficiency. The method is analyzed, and its performance is compared with existing approaches through rigorous experimentation. The results demonstrate the superiority of the proposed modification, making it a promising alternative for solving complex systems of non-linear equations.

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