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Abstract
One of the classical problems in numerical analysis is to find the
solutions of the nonlinear equation f(x)=0 because the
solutions of nonlinear equations are necessary due to their wide range
of appearances in a number of fields, for example, boundary value
problems, dynamic systems are mathematically modeled by difference or
differential equations, chemical engineering, operation research and
many others which involve solving nonlinear equations either
individually or collectively. Iterative methods are used to solve these
nonlinear equations. Recently, due to the development of various
computer software and hardware many iterative methods have been
developed to approximate a solution to nonlinear equations f(x)=0.
In this lecture, we try to present some new modifications in the last
ten years of Newton-Raphson method, and also we derive some new methods
with higher order convergence for solving nonlinear equations f(x)=0.
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