Extended Local Convergence for High Order Schemes Under ω-Continuity Conditions

Authors

  • Gus Argyros Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
  • Michael Argyros Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
  • 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

DOI:

https://doi.org/10.37256/cm.152020709

Keywords:

sixth convergence order, ball of convergence, convergence criteria

Abstract

There is a plethora of schemes of the same convergence order for generating a sequence approximating a solution of an equation involving Banach space operators. But the set of convergence criteria is not the same in general. This makes the comparison between them challenging and only numerically. Moreover, the convergence is established using Taylor series and by assuming the existence of high order derivatives that do not even appear on these schemes. Furthermore, no computable error estimates, uniqueness for the solution results or a ball of convergence is given. We address all these problems by using only the first derivative that actually appears on these schemes and under the same set of convergence conditions. Our technique is so general that it can be used to extend the applicability of other schemes along the same lines.

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Published

2020-12-09

How to Cite

1.
Argyros G, Argyros M, Argyros IK, George S. Extended Local Convergence for High Order Schemes Under ω-Continuity Conditions. Contemp. Math. [Internet]. 2020 Dec. 9 [cited 2024 Mar. 29];1(5):452-61. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/709