Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative

Document Type : Original Article

Authors

Ioannis K. Argyros ¹

Santhosh George ²

Shobha M. Erappa ³

¹ Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

² Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, India

³ Department of Mathematics, Manipal Institute of Technology, Manipal, Karnataka, 576104, India

10.22034/kjm.2019.88082

Abstract

We expand the applicability of eighth order-iterative method studied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Keywords

Eighth order of convergence

ball convergence

Banach space

Frechet-derivative

Subjects

• 65 Numerical analysis

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