A 4th-Order Optimal Extension of Ostrowski’s Method for Multiple Zeros of Univariate Nonlinear Functions

Ramandeep Behl and Waleed M. Al-Hamdan
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Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Waleed M. Al-Hamdan: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2019, vol. 7, issue 9, 1-10

Abstract: We present a new optimal class of Ostrowski’s method for obtaining multiple zeros of univariate nonlinear functions. Several researchers tried to construct an optimal family of Ostrowski’s method for multiple zeros, but they did not have success in this direction. The new strategy adopts a weight function approach. The design structure of new families of Ostrowski’s technique is simpler than the existing classical families of the same order for multiple zeros. The classical Ostrowski’s method of fourth-order can obtain a particular form for the simple root. Their efficiency is checked on a good number of relevant numerical examples. These results demonstrate the performance of our methods. We find that the new methods are just as competent as other existing robust techniques available in the literature.

Keywords: multiple roots; nonlinear equations; Ostrowski’s method; optimal convergence order; efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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