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In this article, an iterative, bracketing and derivative-free method have been proposed with the second-order of convergence for the solution of non-linear equations. The proposed method derives from the Stirling interpolation technique, Stirling interpolation technique is the process of using points with known values or sample points to estimate values at unknown points or polynomials. All types of problems (taken from literature) have been tested by the proposed method and compared with existing methods (regula falsi method, secant method and newton raphson method) and it’s noted that the proposed method is more rapidly converges as compared to all other existing methods. All problems were solved by using MATLAB Version: 8.3.0.532 (R2014a) on my personal computer with specification Intel(R) Core (TM) i3-4010U CPU @ 1.70GHz with RAM 4.00GB and Operating System: Microsoft Windows 10 Enterprise Version 10.0, 64-Bit Server, x64-based processor.
Sanaullah Jamali (Sat,) studied this question.