SOME VARIANTS OF NEWTON’S METHOD WITH ACCELERATED THIRD ORDER CONVERGENCE
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Author:
MUHAMMAD ZAIGHAM MUZAMMAL
Citable URI :
https://vspace.vu.edu.pk/detail.aspx?id=288
Publisher :
Virtual University
Date Issued:
1/9/2020 12:00:00 AM
Abstract
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.
URI :
https://vspace.vu.edu.pk/details.aspx?id=288
Citation:
Muzammal, M.Z(2019). SOME VARIANTS OF NEWTON’S METHOD WITH ACCELERATED THIRD ORDER CONVERGENCE. Virtual University of Pakistan.(Lahore, Pakistan).
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Final Version
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