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Second derivative free sixth order continuation method for solving nonlinear equations with applications
(Journal of Mathematical Chemistry, 2018-08)
In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least ...
An efficient optimal family of sixteenth order methods for nonlinear models
(Journal of Computational and Applied Mathematics, 2018)
The principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ Newton’s method to further develop new interesting optimal ...
An Overview on Steffensen-Type Methods
(Advances in iterative methods for nonlinear equations, 2016)
In this chapter we present an extensive overview of Steffensen-type methods. We first present the real study of the methods and then we present the complex dynamics related this type of methods applied to different ...
Study of local convergence and dynamics of a king-like two-step method with applications
(Mathematics, 2020-07-01)
In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...
Study of a high order family: Local convergence and dynamics
(Mathematics, 2019-03-01)
The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...
Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation
(Journal of Mathematical Chemistry, 2016-08)
We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...
Local Convergence and the Dynamics of a Two-Step Newton-Like Method
(International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2016-05)
We present the local convergence analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.
Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions
(Numerical Algorithms, 2017-02)
We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies ...
A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative
(Numerical Algorithms, 2016-01)
We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...
Convergence and Dynamics of a Higher-Order Method
(Symmetry, 2020-03)
Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves ...