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A large number of problems arise with non linear equations in numerical analysis. To solve such non linear equations several iterative methods have been developed by using different techniques. The aim of this work is to study the improvement in the number of iteration and convergence of Newton-Raphson method to solve a non linear equation ??(??) = 0 by applying modified quadrature rules. These quadratures include Trapezoidal, Simpson one-third, Simpson three-eight and Boole rule. By applying these quadratures some new modified forms of Newton?s method are obtained and their convergence analysis is studied. These variants show third order convergence. Different examples presented illustrate the efficiency of these newly generated variants of Newton?s method when compared with already developed method.
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