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Open AccessFeature PaperArticle

Direct Comparison between Two Third Convergence Order Schemes for Solving Equations

1
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka 575 025, India
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1080; https://doi.org/10.3390/sym12071080
Received: 24 May 2020 / Revised: 29 May 2020 / Accepted: 30 May 2020 / Published: 1 July 2020
(This article belongs to the Special Issue Iterative Numerical Functional Analysis with Applications)
We provide a comparison between two schemes for solving equations on Banach space. A comparison between same convergence order schemes has been given using numerical examples which can go in favor of either scheme. However, we do not know in advance and under the same set of conditions which scheme has the largest ball of convergence, tighter error bounds or best information on the location of the solution. We present a technique that allows us to achieve this objective. Numerical examples are also given to further justify the theoretical results. Our technique can be used to compare other schemes of the same convergence order. View Full-Text
Keywords: banach space; third convergence order schemes; ball convergence; Chebyshev-type scheme banach space; third convergence order schemes; ball convergence; Chebyshev-type scheme
MDPI and ACS Style

Regmi, S.; Argyros, I.K.; George, S. Direct Comparison between Two Third Convergence Order Schemes for Solving Equations. Symmetry 2020, 12, 1080.

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