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Local Comparison between Two Ninth Convergence Order Algorithms for 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 575025, India
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Author to whom correspondence should be addressed.
Algorithms 2020, 13(6), 147; https://doi.org/10.3390/a13060147
Received: 24 May 2020 / Revised: 13 June 2020 / Accepted: 19 June 2020 / Published: 20 June 2020
A local convergence comparison is presented between two ninth order algorithms for solving nonlinear equations. In earlier studies derivatives not appearing on the algorithms up to the 10th order were utilized to show convergence. Moreover, no error estimates, radius of convergence or results on the uniqueness of the solution that can be computed were given. The novelty of our study is that we address all these concerns by using only the first derivative which actually appears on these algorithms. That is how to extend the applicability of these algorithms. Our technique provides a direct comparison between these algorithms under the same set of convergence criteria. This technique can be used on other algorithms. Numerical experiments are utilized to test the convergence criteria. View Full-Text
Keywords: Banach space; high convergence order algorithms; semi-local convergence Banach space; high convergence order algorithms; semi-local convergence
MDPI and ACS Style

Regmi, S.; Argyros, I.K.; George, S. Local Comparison between Two Ninth Convergence Order Algorithms for Equations. Algorithms 2020, 13, 147.

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