Ball comparison between Jarratt‘s and other fourth order method for solving equations

Ioannis K. Argyros; Santhosh George

doi:10.4067/S0719-06462018000300065

DOI:

https://doi.org/10.4067/S0719-06462018000300065

Abstract

The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt‘s fourth order method and another method of the same convergence order.

Keywords

Jarratt method , Banach space , Ball convergence

Ioannis K. Argyros Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
Santhosh George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India.

Pages: 65–79
Date Published: 2019-03-15
Vol. 20 No. 3 (2018)

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