New derivative-free iterative family having optimal convergence order sixteen and its applications. Issue 3 (27th July 2021)

• Record Type: Journal Article
• Authors: Kaur, Manpreet; Kumar, Sanjeev; Kansal, Munish
• Is Part Of: Engineering computations. Volume 39:Issue 3(2022)
• Page Start: 965
• Page End: 992
• Publication Date: 2021-07-27
• Subjects: Iterative methods -- Kung-Traub conjecture -- Chemical equilibrium -- With and without memory methods -- Basins of attraction; 65H05 -- 65Y20; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-03-2021-0155
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of the article is to construct a new class of higher-order iterative techniques for solving scalar nonlinear problems. Design/methodology/approach: The scheme is generalized by using the power-mean notion. By applying Neville's interpolating technique, the methods are formulated into the derivative-free approaches. Further, to enhance the computational efficiency, the developed iterative methods have been extended to the methods with memory, with the aid of the self-accelerating parameter. Findings: It is found that the presented family is optimal in terms of Kung and Traub conjecture as it evaluates only five functions in each iteration and attains convergence order sixteen. The proposed family is examined on some practical problems by modeling into nonlinear equations, such as chemical equilibrium problems, beam positioning problems, eigenvalue problems and fractional conversion in a chemical reactor. The obtained results confirm that the developed scheme works more adequately as compared to the existing methods from the literature. Furthermore, the basins of attraction of the different methods have been included to check the convergence in the complex plane. Originality/value: The presented experiments show that the developed schemes are of great benefit to implement on real-life problems.