 Three novel fifth-order iterative schemes for solving nonlinear equationsChein-Shan Liu, Essam R. El-Zahar and Chih-Wen Chang Mathematics and Computers in Simulation (MATCOM), 2021, vol. 187, issue C, 282-293 Abstract: Kung and Traub’s conjecture indicates that a multipoint iterative scheme without memory and based on m evaluations of functions has an optimal convergence order p=2m−1. Consequently, a fifth-order iterative scheme requires at least four evaluations of functions. Herein, we derive three novel iterative schemes that have fifth-order convergence and involve four evaluations of functions, such that the efficiency index is E.I.=1.49535. On the basis of the analysis of error equations, we obtain our first iterative scheme from the constant weight combinations of three first- and second-class fourth-order iterative schemes. For the second iterative scheme, we devise a new weight function to derive another fifth-order iterative scheme. Finally, we derive our third iterative scheme from a combination of two second-class fourth-order iterative schemes. For testing the practical application of our schemes, we apply them to solve the van der Waals equation of state. Keywords: Nonlinear equations; Constantly weighting technique; Fifth-order iterative schemes; Error equations; Weight function (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:187:y:2021:i:c:p:282-293 DOI: 10.1016/j.matcom.2021.03.002 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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