Title: An optimal class of fourth-order multiple-root finders of Chebyshev-Halley type and their basins of attraction

Authors: Raj Bala; Munish Kansal; Vinay Kanwar

Addresses: Department of Mathematics, Government College, Barwala, Panchkula-134118, India ' School of Mathematics, Thapar Institute of Engineering and Technology, Patiala-147004, India ' Department of Mathematics, University Institute of Engineering and Technology, Panjab University, Chandigarh-160014, India

Abstract: In this paper, we propose a family of optimal fourth-order of Chebyshev-Halley type methods free from second-order derivative for finding the multiple roots. The new methods are tested and compared with other well-known methods on different academical test functions. Further, for quantitative comparison, we have also computed total number of convergent points and convergent percentages, average number of iterations per convergent points and CPU time (in seconds) along with the basins of attraction on number of test problems to recommend the best optimal fourth-order method. We also consider a concrete variety of real life problems such as the trajectory of an electron in the air gap between two parallel plates, van der Waals equation 'which explains the behaviour of a real gas' by introducing in the ideal gas equation, in order to check the applicability and effectiveness of our proposed methods.

Keywords: nonlinear equations; Chebyshev-Halley type methods; multiple roots; efficiency index; optimal order of convergence; basins of attraction.

DOI: 10.1504/IJCSM.2021.118074

International Journal of Computing Science and Mathematics, 2021 Vol.14 No.1, pp.17 - 35

Received: 29 May 2018
Accepted: 07 Dec 2018
Published online: 12 Oct 2021 *

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