Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions

Himani Arora, Alicia Cordero, Juan R. Torregrosa, Ramandeep Behl and Sattam Alharbi
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Himani Arora: Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Sattam Alharbi: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 9, 1-13

Abstract: The construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order techniques. Our schemes are free from derivatives and have been designed to find multiple roots ( m ≥ 2 ). The new techniques involve the weight function approach. The convergence analysis for the new family is presented in the main theorem. In addition, some special cases of the new class are discussed. We also illustrate the applicability of our methods on van der Waals, Planck’s radiation, root clustering, and eigenvalue problems. We also contrast them with the known methods. Finally, the dynamical study of iterative schemes also provides a good overview of their stability.

Keywords: nonlinear equations; Steffensen’s method; multiple roots (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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