Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence

Ioannis K. Argyros; Santhosh George

doi:10.33993/jnaat501-1247

Authors

Ioannis K. Argyros Cameron University, USA
Santhosh George NIT Karnataka, India

DOI:

https://doi.org/10.33993/jnaat501-1247

Keywords:

Potra-Ptak-type method, Newton's method, order of convergence, local convergence

Abstract views: 239

Abstract

We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used.

In this paper we use hypotheses up to the first derivative only, so that the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.

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