Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Ramandeep Behl, Sonia Bhalla, Eulalia Martínez and Majed Aali Alsulami
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Ramandeep Behl: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Sonia Bhalla: Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, India
Eulalia Martínez: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain
Majed Aali Alsulami: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2021, vol. 9, issue 11, 1-14

Abstract: There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots ( m ? 2 ) . In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

Keywords: King’s method; nonlinear equations; optimal iterative methods; multiple roots; Kung–Traub conjecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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