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Different modifications in the Newton's method with cubic convergence have become popular iterative methods to find the roots of non-linear equations. In this paper, a modified Newton's method for solving a single nonlinear equation is proposed. This method uses harmonic mean while using Simpson's integration rule, thus replacing ′ in the classical Newton's method. The convergence of the proposed method is found to be order three. Numerical examples are provided to compare e the efficiency ofdoi:10.9790/5728-0749397 fatcat:f2kzry6ubvfrvlhetn5wpv74na