Abstract
Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family of third-order derivative-free iterative methods for multiple zeros that require only evaluations of three functions per iteration. Convergence of the proposed class is demonstrated by means of using a graphical tool, namely basins of attraction. Applicability of the methods is demonstrated through numerical experimentation on different functions that illustrates the efficient behavior. Comparison of numerical results shows that the presented iterative methods are good competitors to the existing techniques.
Highlights
We introduce a two-step family of third-order derivative-free methods for computing multiple zeros that require three evaluations of the function f per iteration
First we plot the basins of attraction of the zeros of some polynomials when the proposed iterative methods are applied on the polynomials
From the numerical results we examine that the accuracy in the values of successive approximations rises, which shows the stable nature of the methods
Summary
Have been proposed and verified in the literature; see, for example: [2,3,4,5,6,7,8,9,10,11,12,13,14,15] and references therein Such methods require the evaluations of derivatives of either linear order or linear and second order, or both. We introduce a two-step family of third-order derivative-free methods for computing multiple zeros that require three evaluations of the function f per iteration. Many special methods of the family can be generated depending on the forms of weight factors Efficacy of these methods is tested on various numerical problems of different natures.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
