Abstract
In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods.
Highlights
Many iterative methods for solving nonlinear equations often include non-zero free parameters
The main goal of this paper is to find the optimal choices of parameters ττnn and, γ in the two points iterative methods
We present the results of numerical experiments that confirm the theoretical conclusion about the convergence order and made a comparison with well-known methods of the same order of convergence
Summary
Many iterative methods for solving nonlinear equations often include non-zero free parameters. Their suitable choices allow to increase the convergence order of methods. Optimization by parameters is one of the powerful techniques in science and engineering practice. The main goal of this paper is to find the optimal choices of parameters ττnn and, γ in the two points iterative methods. In numerical analysis and engineering applications, it is often required to solve a nonlinear equation f (x) = 0, where f (x) : D ⊂ R → R is a scalar function defined on an open interval D.
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