Extending the Convergence of Two Similar Sixth Order Schemes for Solving Equations under Generalized Conditions

Authors

  • 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 https://orcid.org/0000-0002-3530-5539
  • Christopher I. Argyros Department of Computing and Technology, Cameron University, OK 73505, USA

DOI:

https://doi.org/10.37256/cm.242021991

Keywords:

seventh convergence order, ω-continuity, local convergence, Banach space

Abstract

The applicability of two competing efficient sixth convergence order schemes is extended for solving Banach space valued equations. In previous works, the seventh derivative has been used not appearing on the schemes. But we use only the first derivative that appears on the scheme. Moreover, bounds on the error distances and results on the uniqueness of the solution are provided not given in the earlier works based on ω-continuity conditions. Our technique extends other schemes analogously, since it is so general. Numerical examples complete this work.

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Published

2021-08-26

How to Cite

1.
Ioannis K. Argyros, George S, Argyros CI. Extending the Convergence of Two Similar Sixth Order Schemes for Solving Equations under Generalized Conditions. Contemp. Math. [Internet]. 2021 Aug. 26 [cited 2024 Jul. 18];2(4):246-57. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/991