An Efficient Four Step Fifteenth Order Method for Solution of Non-Linear Models in Real-World Problems - Sanaullah Jamali; Zubair Ahmed Kalhoro; Imran Qasim Memon (Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 2024)
Non-linear equations are fundamental to a wide range of practical applications in engineering and applied sciences. This research paper presents a novel iterative scheme—a fifteenth-order approach—designed to effectively solve non-linear problems. The numerical results of the Proposed Scheme are thoroughly compared with those of existing methods. Graphical representations and basin of attraction analysis reveal that the fifteenth-order method achieves superior accuracy and efficiency, surpassing alternative methods in the precise estimation of solutions to non-linear problems.