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Symmetry
Volume 11
Issue 2
10.3390/sym11020128
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Article

Two-Step Solver for Nonlinear Equations

by
Ioannis K. Argyros
1,
Stepan Shakhno
2,* and
Halyna Yarmola
2
1
Department of Mathematics, Cameron University, Lawton, OK 73505, USA
2
Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Universitetska Str. 1, Lviv 79000, Ukraine
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(2), 128; https://doi.org/10.3390/sym11020128
Submission received: 23 December 2018 / Revised: 14 January 2019 / Accepted: 18 January 2019 / Published: 23 January 2019
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
Versions Notes

Abstract

In this paper we present a two-step solver for nonlinear equations with a nondifferentiable operator. This method is based on two methods of order of convergence 1 + 2 . We study the local and a semilocal convergence using weaker conditions in order to extend the applicability of the solver. Finally, we present the numerical example that confirms the theoretical results.
Keywords: Nondifferentiable operator; nonlinear equation; divided difference; Lipschitz condition; convergence order; local and semilocal convergence Nondifferentiable operator; nonlinear equation; divided difference; Lipschitz condition; convergence order; local and semilocal convergence

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MDPI and ACS Style

Argyros, I.K.; Shakhno, S.; Yarmola, H. Two-Step Solver for Nonlinear Equations. Symmetry 2019, 11, 128. https://doi.org/10.3390/sym11020128

AMA Style

Argyros IK, Shakhno S, Yarmola H. Two-Step Solver for Nonlinear Equations. Symmetry. 2019; 11(2):128. https://doi.org/10.3390/sym11020128

Chicago/Turabian Style

Argyros, Ioannis K., Stepan Shakhno, and Halyna Yarmola. 2019. "Two-Step Solver for Nonlinear Equations" Symmetry 11, no. 2: 128. https://doi.org/10.3390/sym11020128

APA Style

Argyros, I. K., Shakhno, S., & Yarmola, H. (2019). Two-Step Solver for Nonlinear Equations. Symmetry, 11(2), 128. https://doi.org/10.3390/sym11020128

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