In this paper, we present some new third-order iterative methods for finding a simple root α
of nonlinear scalar equation f (x)= 0 in R. A geometric approach based on the circle of …

For solving non-linear equations, iterative root-finding methods are important because of the
broad range of applications in science and engineering. We have constructed an iterative …

In this paper, a unified point of view that includes the most of one-point Newton-type iterative
methods for solving nonlinear equations is introduced. A simple idea to design iterative …

In this work, we develop nine derivative-free families of iterative methods from the three well-
known classical methods: Chebyshev, Halley and Euler iterative methods. Methods of the …

One‐parameter families of Newton′ s iterative method for the solution of nonlinear
equations and its extension to unconstrained optimization problems are presented in the …

In this paper, we present a new iterative method to solve systems of nonlinear equations.
The main advantages of the method are: it has order three, it does not require the evaluation …

In this paper, we present many new fourth-order optimal families of Jarratt's method and
Ostrowski's method for computing simple roots of nonlinear equations numerically. The …

In this paper, we derive one-parameter families of Newton, Halley, Chebyshev, Chebyshev-
Halley type methods, super-Halley, C-methods, osculating circle and ellipse methods …

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In this paper two families of zero-finding iterative methods for solving nonlinear equations f
(x)= 0 are presented. The key idea to derive them is to solve an initial value problem …