Here, we suggest a high-order optimal variant/modification of Schroder's method for obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically convergent Schroder'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.

A New Optimal Family of Schröder’s Method for Multiple Zeros / Ferrara, Massimiliano; Behl, R; Alsolami, A. J.; Pansera, B. A.; Al-Hamdan, W. M.; Salimi, M. - In: MATHEMATICS. - ISSN 2227-7390. - 1076:7(11)(2019), pp. 1-14. [doi.org/10.3390/math7111076]

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

FERRARA, Massimiliano
Supervision
;
Pansera B. A.
Writing – Original Draft Preparation
;
2019-01-01

Abstract

Here, we suggest a high-order optimal variant/modification of Schroder's method for obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically convergent Schroder'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.
2019
efficiency index; nonlinear uni-variate functions; Schroder's method; optimal order of convergence
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/898
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