A New Optimal Family of Schröder’s Method for Multiple Zeros

Ramandeep Behl, Arwa Jeza Alsolami, Bruno Antonio Pansera, Waleed M. Al-Hamdan, Mehdi Salimi and Massimiliano Ferrara
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Ramandeep Behl: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Arwa Jeza Alsolami: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Bruno Antonio Pansera: Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
Waleed M. Al-Hamdan: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Mehdi Salimi: Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
Massimiliano Ferrara: Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy

Mathematics, 2019, vol. 7, issue 11, 1-14

Abstract: Here, we suggest a high-order optimal variant/modification of Schröder’s method for obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically convergent Schröder’s method, we derive the new family of fourth -order multi-point methods having optimal convergence order. Additionally, we discuss the theoretical convergence order and the properties of the new scheme. The main finding of the present work is that one can develop several new and some classical existing methods by adjusting one of the parameters. Numerical results are given to illustrate the execution of our multi-point methods. We observed that our schemes are equally competent to other existing methods.

Keywords: efficiency index; nonlinear uni-variate functions; Schröder’s method; optimal order of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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