Adnan Ali Mastoi ,Muhammad Mujtaba Shaikh,Abdul Wasim Shaikh,




Convergence,Efficiency,Nonlinear equation,Derivative-based,Precision,


In this study, a new derivative-based cubically convergent iterative method is established for nonlinear equations, which is a modification of an existing method. The idea of difference quotient is used to arrive at a better formula than the existing one. The theorem concerning the order of convergence has been proved theoretically. Some examples of nonlinear equations have been solved to analyse convergence and competence of the PM against existing methods. High precision arithmetic has been used and graphs have been plotted using Ms Excel. Using standard test parameters: efficiency index, absolute error distributions, observed order of convergence, number of iterations and number of evaluations, the PM is compared against the existing methods, and is found to be a cost-efficient alternative with the higher order of convergence. From results, it has been detected that established technique is superior to the widely used Bisection (BM), Regula-Falsi (RFM) and Newton-Raphson (NRM) methods from iterations and accuracy perspectives. Moreover, the proposed method (PM) is cost-efficient than the original method used for modification as well as some other methods.


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