On the convergence of Kurchatov-type methods using recurrent functions for solving equations

  • I. K. Argyros Department of Mathematical Sciences, Cameron University, Lawton, USA
  • S. Shakhno Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Lviv, Ukraine
  • H. Yarmola Department of Computational Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine
Keywords: nonlinear equation; Kurchatov's method; Banach space; divided difference; local and semi-local convergence; two-step method

Abstract

We study a local and semi-local convergence of Kurchatov's method and its two-step modification for solving nonlinear equations under the classical Lipschitz conditions for the first-order divided differences. To develop a convergence analysis we use the approach of restricted convergence regions in a combination to our technique of recurrent functions. The semi-local convergence is based on the majorizing scalar sequences. Also, the results of the numerical experiment are given.

Author Biographies

I. K. Argyros , Department of Mathematical Sciences, Cameron University, Lawton, USA

Department of Mathematical Sciences,
Cameron University, Lawton, USA

S. Shakhno, Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Lviv, Ukraine

Department of Theory of Optimal Processes,
Ivan Franko National University of Lviv, Lviv, Ukraine

H. Yarmola, Department of Computational Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine

Department of Computational Mathematics,
Ivan Franko National University of Lviv, Lviv, Ukraine

References

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Published
2022-10-31
How to Cite
Argyros , I. K., Shakhno, S., & Yarmola, H. (2022). On the convergence of Kurchatov-type methods using recurrent functions for solving equations. Matematychni Studii, 58(1), 103-112. https://doi.org/10.30970/ms.58.1.103-112
Section
Articles